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# Validity of proportion estimate from finite sample

If I have a batch of 130 parts and I inspect a random sample of 14 parts, either accept or reject the part, and calculate the percent defective in the sample, how confident can I be that the percent defective in the sample represents the percent defective in the batch?

Here's why I need to know: We have a process with very poor capability - generally around 20% defective. We want to pull a sample as soon as a batch of 130 parts is done and be able to predict the yield with some confidence level so we can react by either continuing to run if less than 20% defective would be expected from the batch within our confidence interval or shut down if greater than 20% defective is expected based on the sample. I will be asked how confident am I that the sample yield represents the final batch yield. P.S. I am not a statistician, but I have taken a lot of engineering mathematics.

• Not sure what exactly you are looking for. But if your question is answered by "I'm 95% certain that in 95% of the 130 part samples the number of defective parts will be between x and y" then you need to look up tolerance intervals. Jan 20 '14 at 19:30
• what does the word 'represent' really mean in this context? A precise definition of what kind of statement you want to make might help pin things down. Jan 20 '14 at 20:42

This is more of a comment, but I don't quite have enough reputation points to commend ;)

You'll never get a confidence that the rate is exactly some number - it's actually zero that it will be any particular exact real number (of which there are an uncountably infinite number in any interval).

What you can do with your sample of 14 is create a confidence that the population defect rate is more or less than some threshold. Suppose you want no more than 12% defects. Depending upon how confident you need to be, you can sample fewer or more, and obviously sampling more will give you greater confidence. Furthermore, the more conservative your threshold, the more confidence can be developed for a given sample size. With 14 samples, the defect rate will probably be 0%, maybe 7.14%, hopefully not 14.28% or higher. But since other intermediate probabilities are not possible from a sample size of 14, you can see how much uncertainty exists. Since 14 is not a factor of 130, the probabilities (in the sense of rate, not a chance over a larger population) cannot possibly be precisely equal.

Assuming a 20% defect rate in the batch/population, you can use a binomial to calculate the probabilities of each potential number of defects in the sample. I get: defects prob cum prob

     0    0.0440    0.0440
1.0000    0.1539    0.1979
2.0000    0.2501    0.4481
3.0000    0.2501    0.6982
4.0000    0.1720    0.8702
5.0000    0.0860    0.9561
6.0000    0.0322    0.9884
7.0000    0.0092    0.9976
8.0000    0.0020    0.9996

rest of table has very low probabilities

So, if you only find no defects in your sample of 14, you can be 1-0.044 or 95.6% sure that the overall defect rate is less than 20%. However, if you get 2 defects out of 14, the confidence is only about 55% - still probable (>50) which is intuitive since 2/14 <0.2.

However, if you increased you sample to 28, the table would become:

     0    0.0019    0.0019
1.0000    0.0135    0.0155
2.0000    0.0457    0.0612
3.0000    0.0990    0.1602
4.0000    0.1547    0.3149
5.0000    0.1856    0.5005
6.0000    0.1779    0.6784
7.0000    0.1398    0.8182
8.0000    0.0917    0.9100
9.0000    0.0510    0.9609

10.0000 0.0242 0.9851 11.0000 0.0099 0.9950 12.0000 0.0035 0.9985 13.0000 0.0011 0.9996 14.0000 0.0003 0.9999 15.0000 0.0001 1.0000

Now a sample defect number of 4 (4/28 is the same rate as 2/14) gives you a better confidence, about 68%, of a population defect rate of less than 20%.

Thanks whuber!

Revised for sample size 14 with they hypergeometric

numDefects prob cumProb

     0    0.0364    0.0364
1.0000    0.1455    0.1819
2.0000    0.2570    0.4388
3.0000    0.2653    0.7041
4.0000    0.1785    0.8826
5.0000    0.0827    0.9653
6.0000    0.0271    0.9924
7.0000    0.0064    0.9988
8.0000    0.0011    0.9999
9.0000    0.0001    1.0000

• Thanks for the feedback. I understand pretty much the situation as you desribe it. Maybe this would help clarify - here's my reason for wanting to know: Jan 20 '14 at 19:21
• (1) This is a finite population situation, so a hypergeometric calculation would be more accurate (although the binomial is a decent approximation). For instance, the value for $0$ is $0.0364$ rather than $0.0440$. This has a more profound effect for larger samples. (2) Your answer seems to use "confidence" in the sense of "probability": that is not the usual meaning unless you are performing a Bayesian analysis, but you're not doing that.
– whuber
Jan 21 '14 at 17:33


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A seemingly simple triple integral has me stumped

1. Jan 29, 2009

Seda

1. The problem statement, all variables and given/known data

Essentially, do the volume integral of z^2 over the tetrahedron with vetices at (0,0,0) (1,0,0) (0,1,0) (0,0,1)

3. The attempt at a solution

There seems to be a ton(!) of brute-force algebra involved. Enough to make me question if I'm doing the problem right.
I set up the triple integral of z^2 in the order dzdydx with the following limits of integration.

z=0 to z= 1-x-y
y=0 to y= 1-x
x=0 to x=1

It didn't take to long for me to end up with trying to integrate a humongous polynomial in the second interval.

Evaluating z^3 / 3 at z = 1-x-y was fun enough.

But now after integrating again, I have to evaluate y/3 -xy-y^2/2+xy^2+x^2*y + y^3/3 + 1/3*x^3*y et cetera at y = 1-x seems to be a nightmare.

Am I tackling this the wrong way?

2. Jan 29, 2009

Dick

No, I think your approach is correct. Though I'm not sure I agree with your xy polynomial. You just have to work through the mess and be careful. If don't have to use a triple integral you can use a shortcut. If A(z) is the area of a cross section of the tetrahedron at a constant value of z, and you can use geometry to get a formula for that area in terms of z, then the triple integral is the integral of A(z)*z^2*dz. Hmm. That sort of suggests that you change the order of integration so you integrate over z last, it might be easier.

3. Jan 29, 2009

Seda

Yeah not only have I found a few mistakes, but i typed some parts in wrong, I was really just writing the polynomial to show how ugly.

Ill try integrating over x last then.

4. Jan 29, 2009

Dick

Z last, I think. You already did X last.

5. Jan 29, 2009

Seda

sorry, i meant z

6. Jan 29, 2009

Seda

Ok i have an answer now, thanks for the help.

Yes, integrating in the different order helped alot. Much cleaner algebra there.

7. Jan 29, 2009

Dick

Right. If your integrand depends on a subset of the variables, integrate over those variables last. It keeps them constants for as long as possible.

format: plain


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SEARCH HOME
 Math Central Quandaries & Queries
 Question from Shelby, a student:& Find exact value of x for 1 <(or equal to) x < 2pi a) cos(x) = -1/(square root of 2)

Hi Shelby,

I find that the circle approach is the best way to approach this type of problem. Draw a circle with radius 1 unit and center at the origin $O.$ Draw a line segment from $O$ to a point $P$ on the circumference of the circle and measure the angle counterclockwise from the positive X-axis to the line segment $OP.$ If the measure of this angle is $t$ radians then $P$ has coordinates $\left(\cos(t), \sin(t)\right).$

You want the measure of the angle $t$ so that $\cos(t) = \frac{-1}{\sqrt 2}.$ Since $\cos(t)$ is the X-coordinate I drew the line $x = \frac{-1}{\sqrt2}$ to see where this line intersects the circle. There are two points $Q$ and $R$ in the diagram so there are two angles with measures $t_1$ and $t_2$ that have $\cos(t_1) = \cos(t_2) = \frac{-1}{\sqrt 2}.$

Let's look at $t_1$ more carefully.

Triangle $QSO$ is a right triangle, the length of $OQ$ is 1 unit and the length of $SP$ is $\frac{1}{\sqrt2} \mbox{ units.}$ Use Pythagoras theorem to find the length of $QS.$ What does that tell you about the triangle $QOS?$ What is the measure of the angle $SOQ?$ What is the angle measure $t_1?$

Apply a similar approach to fine the angle measure $t_2.$

I hope this helps,
Penny

Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.


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# PYME.Analysis.PSFEst.psfQuality module¶

These functions assess a psf for quality and return a scalar ‘merit’ which indicates how good or bad the psf is wrt the particular measure.

Lower values are better, with the following breakpoints:

merit < 1 good OK to use 1 < merit < 2 marginal Might work in some situations but undesirable - use with caution merit > 3 unacceptable Almost garuanteed not to work
PYME.Analysis.PSFEst.psfQuality.background(image, psft)

This test uses the fact that the PSF should not extend to at edge of the image to judge background levels by looking at the mean values of the pixels along one edge. It assumes the PSF is normalised to a peak intensity of 1 (which it should be if extracted using the normal tools).

PYME.Analysis.PSFEst.psfQuality.colour(merit)
PYME.Analysis.PSFEst.psfQuality.crb3d(image, psft)

The Cramar-Rao bound describes the ammount of position information encoded in a PSF. This test computes the average 3D CRB (the vector norm of the 3 individual axis CRBs) over a 1 um depth range and compares it to that obtained from a simulated astigmatic PSF with 500nm lobe separation. The PSF is classed as good if the 3D CRB is less than twice that of the simulated PSF.

PYME.Analysis.PSFEst.psfQuality.dec_test(fcnName)
PYME.Analysis.PSFEst.psfQuality.depth_dec(image, psft)

Deconvolution needs a PSF which is at least 5-6 times the axial resolution of the data set and preferably as large as the stack to be deconvolved. In practice this means that the PSF should be at least 5 um deep.

PYME.Analysis.PSFEst.psfQuality.depth_loc(image, psft)

A psf used for 3D localisation should be sufficiently deep to capture the regions of the PSF which retain sufficient intensity to allow reasonable detection and localisation. In practice, a total range of 2-3um should be sufficient. Due to the implementation of the object finding algorithm, very large axial extents are actually a disadvantage as they will interfere with reliable event detection.

PYME.Analysis.PSFEst.psfQuality.glob_test(fcnName)
PYME.Analysis.PSFEst.psfQuality.loc_test(fcnName)
PYME.Analysis.PSFEst.psfQuality.noise(image, psft)

This test looks at a region to the side of the in-focus plane to assess noise levels. Noise can be improved by using a longer integration time when acquiring the bead images or by averaging more beads.

PYME.Analysis.PSFEst.psfQuality.positivity(image, psft)

The PSF should not contain any negative values

PYME.Analysis.PSFEst.psfQuality.runTests(image, psft)
PYME.Analysis.PSFEst.psfQuality.size_x(image, psft)

The extracted image should be large enough to capture the PSF, with a fair bit of wriggle room on either side. The default of 61 pixels does this in most situations. Smaller PSFs might work, but are are not guaranteed to - use with caution.

PYME.Analysis.PSFEst.psfQuality.voxelsize_x(image, psft)

The x pixel size should be sufficiently small to Nyquist the PSF. Making the pixels too large looses information whilst making them too small is empty magnification and is incurs extra noise and computational cost. A high NA oil immersion objective is assumed in these calculations

PYME.Analysis.PSFEst.psfQuality.voxelsize_z_dec(image, psft)

z spacing in psfs for deconvolution purposes should match the data spacing, which should be at Nyquist for the expected frequency content of the PSF. If abberated, PSFs will contain frequencies beyond the simple FWHM/2.35 calculalation typically used for voxel size selection. In most cases a z-spacing of 200 nm will be appropriate for a high NA oil immersion objective, although this might sometimes want to be reduced.

PYME.Analysis.PSFEst.psfQuality.voxelsize_z_loc(image, psft)

3D localisation microscopy relies on capturing subtle variations in pixel shape. Although these should nominally be captured in a Nyquist sampled PSF, it is wise to oversample in z (typically using 50 nm spacing) in order to reduce the sensitivity of psf shape to the interpolation algortihms used in the fitting. Oversampling also increases the effective SNR of the PSF


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# In what order did Mendeleev arrange the elements in his periodic table ?

Feb 11, 2018

In order of atomic mass.

#### Explanation:

Mendeleev ordered his elements in his periodic table in the order of atomic mass. What he found by this is that similar elements were grouped together. However, some elements didn't apply to this rule, most notably the isotope forms of elements.

However, our periodic tables differs from Mendeleev's as we order the elements based on atomic number, which puts similar elements in groups based on their chemical properties instead of their looks. Of course, at the time Mendeleev couldn't order based on atomic number as he wasn't able to count the electron/proton number.

Feb 11, 2018

In his periodic table, Mendeleev arranged the elements by atomic weight (relative atomic mass)

#### Explanation:

Nowadays, we arrange the elements according to atomic number, but that information was not available in 1869.

1869 was the year that Russian chemist Dmitri Mendeleev (1834-1907) published his Periodic "System" of the elements.

According to the .org website www.rsc.org/education/
"Other people, like Londoner John Newlands, Frenchman Alexandre Béguyer de Chancourtois, and German Julius Lothar Meyer made important contributions to the first Periodic Table but the main credit goes to Mendeleev."

Here's a picture of a shaggy Mendeleev looking like a mad scientist

Mendeleev's genius idea was to list the elements left to right in rows according to mass, and also from top to bottom in columns according to their properties.

Mendeleev wasn't deterred by the poor quality of the data at that time.

• Only about 50 elements were known

• In some cases, their relative atomic masses were miscalculated

• There were gaps where some elements were missing -- not yet discovered.

• The atomic mass isn't a good metric because it can cause elements to get out of place

But Mendeleev was convinced that listing the elements according to their properties in $\text{columns}$ would create a "double entry" table with their atomic masses going across in $\text{rows}$.

Therefore, when the use of atomic mass instead of atomic number incorrectly located iodine before tellurium, he knew enough to switch them anyway because of the properties of iodine.

Another mathematical difficulty placed beryllium between carbon and nitrogen, where there was no space for it. Mendeleev simply changed the math in order to get beryllium into its correct slot in the periodic table.

Most important was Mendeleev's predictions of elements as yet unknown. There were gaps in the table he created, but not only did he correctly predict that elements would be discovered that filled those gaps, he also predicted their properties.

Three such predictions were proved correct in Mendeleev's lifetime, and two other elements that he predicted were found fifty years later.

Here is a color-coded periodic table that is useful and also quite beautiful

You can see it larger here:
https://sciencenotes.org

Here's a TED site where you can find out more about the periodic table
https://ed.ted.com/lessons/the-genius-of-mendeleev-s-periodic-table-lou-serico


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# zbMATH — the first resource for mathematics

Variational methods for problems from plasticity theory and for generalized Newtonian fluids. (English) Zbl 0964.76003
Lecture Notes in Mathematics. 1749. Berlin: Springer. vi, 269 p. (2000).
The monograph is devoted to a rigorous mathematical analysis of variational problems describing the equilibrium configuration of certain types of perfect elastoplastic solids, and also the stationary flows of some incompressible generalized Newtonian fluids. The authors concentrate on variational problems from the deformation theory of plasticity and on fluid models whose stress-strain relation can be formulated in terms of dissipative potential. The mathematical form of both problems is very close, and is reduced to the study of variational integrals with convex integrands depending only on the symmetric part of gradients of unknown vector-valued functions. The integrands have the linear growth, and the problem of finding suitable classes of admissible deformations is not trivial. Another difficulty of the considered problems consists in their formulations in non-reflexive spaces.
The authors attack these problems by formulating a dual variational problem for the stress tensor, and by the relaxation method. Chapter 1 contains a general scheme for the relaxation of convex variational problems being coercive on some non-reflexive spaces like $$L^1$$ or $$W^1_1$$. The authors give a detailed description of the approach to the perfect plasticity. Besides plasticity with power hardening and perfect plasticity, the authors investigate here the model with logarithmic hardening. Hence the integrand is not of power growth, and it is necessary to introduce new function spaces for localization of solutions. Chapter 2 presents an analysis of regularity of weak solutions. The problems of regularity for integrands with linear growth and for vector-valued functions have been till now discussed only in a few papers. The approach of the authors is based on the study of dual variational problem for stresses. They obtain additional regularity for stress tensor, and with the help of duality relations establish the regularity of displacement field.
The local regularity of solutions to variational problems describing stationary flow of generalized Newtonian fluids is studied in chapter 3. The presentation includes also the viscoplastic fluids of Bingham type. The authors derive partial regularity in spite of the fact that the dissipative potential is not smooth. All investigations are limited to incompressible flows, i.e. only fields with vanishing divergence are considered. Chapter 4 presents the regularity theory for the logarithmic case. Here the authors introduce special functional spaces, and for plasticity with logarithmic hardening they investigate directly the minimizing deformation field. A lot of various results on function spaces is proved in the appendices A and B, and a special chapter is devoted to inevitable tools from functional analysis. The book presents a very complex view-point on the plasticity and fluid mechanics problems. The mechanical and physical phenomena are explained by rigorous mathematical methods, and the potential reader is acquainted with a unified approach to plasticity and fluid mechanics problems in their full complexity.

##### MSC:
 76-02 Research exposition (monographs, survey articles) pertaining to fluid mechanics 74-02 Research exposition (monographs, survey articles) pertaining to mechanics of deformable solids 74G65 Energy minimization in equilibrium problems in solid mechanics 76A05 Non-Newtonian fluids 76M30 Variational methods applied to problems in fluid mechanics 74C05 Small-strain, rate-independent theories of plasticity (including rigid-plastic and elasto-plastic materials)
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# Integration with using Gauss law

Task: find the vector $\mathbf E$ in the center of the sphere with radius $R$, which has charge volume distribution $\rho , \rho = (\mathbf a \cdot \mathbf r ), \mathbf a = \operatorname{const}, \mathbf r$ - radius-vector from the center of the sphere.

My solution: I used Gauss theorem, $$\oint \mathbf E \cdot d\mathbf S = \int \nabla \cdot \mathbf E dV = 4\pi \int\rho\ dV = 4\pi a \int r\cos(\mathbf a , \mathbf r)\ dV .$$ Unfortunately, I don't know how to find $\mathbf E$ using written above: $|\mathbf E| \neq const$ into the surface of the sphere, so I can't write something like $$\oint \mathbf E \cdot d \mathbf S = E \int dS = ...$$ and equate it to (1).

Can you help me?

I created a routinely solution. In the beginning

1. I can consider only surface of the sphere with surface denstity $\rho (S) = (\mathbf a \cdot \mathbf r)$.

2. I "moved" $\mathbf a$ to the center of the sphere by parallel transfer (look to the picture 1 below).

So, I can divide the sphere into thin rings with charge $$dQ = \rho (S)dS = \rho (S) 2\pi r Rd\varphi$$ (R - length from the ring to the center of the sphere, a - length from the ring plane to the center of the sphere, $\varphi$ - an angle between $\mathbf a , \mathbf R$, and $\mathbf r = \sqrt{R^{2} - a^{2}})$. Using that, $d|\mathbf E|$ creating by this ring in the center of the sphere (using the formula for the ring E = \frac{kaQ}{R}), can be write as $$dE = \frac{kadQ}{R^{3}} = \frac{ak\rho (S) 2\pi r R d\varphi}{R^{3}}.$$ According to the spherical symmetry, $$d\mathbf E_{center} = -\frac{\mathbf a}{a}dE,$$ so, according, that $$r = Rsin(\varphi ), \quad a = Rcos(\varphi ), \quad \rho (S) = (\mathbf a \cdot \mathbf r) = aRcos(\varphi ),$$ I get $$d\mathbf E = -\frac{k R cos(\varphi) R cos(\varphi ) 2\pi R sin(\varphi) R d\varphi}{R^{3}}\mathbf a = -2\pi k R cos^{2}(\varphi )sin(\varphi)\mathbf a \Rightarrow$$

$$\Rightarrow \mathbf E = 2\pi k \mathbf a \int \limits_{-1}^{1}cos^{2}(\varphi )d(cos(\varphi )) = \frac{4 \pi k R \mathbf a}{3}.$$ By the next step I accept, that R is a variable (takes into account the volume distribution of charge), so, with the new vector $\mathbf a$ (formally, it's changed only by a dimension, $[|\mathbf a_{new}|] = \frac{[|\mathbf a_{old}|]}{meter}$), $$d\mathbf E = \frac{4 \pi k RdR}{3}\mathbf a \Rightarrow \mathbf E = \frac{2\pi k R^{2}}{3}\mathbf a.$$

-
Two questions: 1) Why do you assume E is constant on the surface of the sphere? 2) Why are you integrating to the surface of the sphere when it is E at the center that you seek? –  Robert Miller Sep 4 '12 at 18:38
Oh yes, I made a mistake. I forgot about a scalar product. –  John Taylor Sep 4 '12 at 18:45
That charge density is interesting. What's the total charge? –  James S. Cook Sep 4 '12 at 18:47
So, this task cannot be solved by using Gauss law? –  John Taylor Sep 4 '12 at 18:47
"...I was reading that as a dot-product :)..." It was a dot product with $\mathbf a = const$ as a vector. Maybe I didn't understand your words. [:(]. –  John Taylor Sep 4 '12 at 18:51


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# 17-21-024

diffraction

deviation of the direction of propagation of radiation, determined by the wave nature of radiation, and occurring when the radiation passes the edge of an obstacle

Note 1 to entry: This entry was numbered 845-01-13 in IEC 60050-845:1987.

Note 2 to entry: This entry was numbered 17-301 in CIE S 017:2011.

Publication date: 2020-12


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Notation for lengths

I've noticed that when you set length, you can not only write \setlength{X}{3.14cm} but \setlength{X}{=3.14cm} as well. It looks like there is not any difference between those notations but I'd like to know why there is a possibility to use notation with "=" sign.

• You could as well type \setlength{\X}{\@firstoftwo{3.14}{Hey! It's pi}cm} if in a \makeatletter context, but this doesn't mean you should. ;-) – egreg Oct 23 '16 at 19:30
• how did you notice that?????? (without starting from the implementation and just inferring that the = would drop through by accident? )Surely no documentation suggests that does it? – David Carlisle Oct 23 '16 at 22:53
• @DavidCarlisle I knew \setlength{X}{Y} expands to {X Y\relax} (I've read it in documentation) and then when experimenting with those notations I discovered the possibility of using =. – Bartłomiej Sługocki Oct 24 '16 at 9:22

\setlength is a LaTeX macro which is defined as:

\def\setlength#1#2{#1 #2\relax}

So \setlength{\mylength}{1cm} expands to \mylength 1cm.

\mylength 1cm

 \mylength=1cm

• @BartłomiejSługocki Other than the TeX Book itself, (which is not freely available), the best free source for TeX itself is Victor Eijkhout's TeX by Topic which you can find using texdoc in your distribution. For the source documentation of the LaTeX kernel, you can look at source2e, also available as part of your distribution via texdoc. – Alan Munn Oct 23 '16 at 19:25


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# Math Help - Interior points proof

1. ## Interior points proof

Any hints or clues appreciated.

Here are my answers so far:

a) if A ∩ S is emtpy then ∅ ∈ ΩS

b) Since A ∈ ΩX(which means A is open), there exists r>0 s.t B(x,r) ⊂ U therfore x ∈ intxA.

c) Don't know

Suppose x ∈ (intxA) ∩ S....

d)?
e)?
f) U is an open set
g) All open sets can be expressed as a union of balls
h) ?

2. Frankly I am tired of dealing with the way you post questions.
It is a waste of time on your part as well as our part.
This current question is unreadable at best.
Why do you think that any of us ought to know what $\Omega S$ means? What is $A~?$
Moreover, you have posted an image that actually cuts-off the given in the question. Do you fear being caught cheating by one of the net-search programs that check for copying?

http://www.mathhelpforum.com/math-he...ial-19060.html
Why not learn to post in symbols? You can use LaTeX tags
Here is an example.
[tex]\Omega S[tex] gives $\Omega S$

3. Sorry thought that this notation was standard...
ΩX = The set af all open sets in X
ΩS = The set af all open sets in S

These are tutorial questions, not any assignment questions(we only write tests), so cheating not an issue, there are no marks invovled... The top part which is cut-off.. has nothing to do with the question.


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# If almost all variance is explained by the few first principal components, what can we say about the dataset?

What can we say about a dataset if we apply PCA and observe that there is a high percentage of variance in the first principal component(s)?

Can we say that this dataset has linear structure? Can we say that most of the features in this dataset are highly correlated?

For example, I extracted PC1 and PC2 for two high-dimensional datasets $A$ and $B$. For data set $A$, 95% of variance is explained by PC1 and PC2. Whereas for data set $B$, we only observed 40% of variance explained by PC1 and PC2. What can we infer about datasets $A$ and $B$?

• Welcome to Cross Validated. In order to allow our users to help you, you need to add more details to your post. Can you post some of your output here so that we know what you're dealing with? A screengrab is fine. – Marquis de Carabas May 3 '16 at 23:11
• @amoeba, the question has since been edited to add information about what the OP meant by "high percentage." I also didn't understand the "linearly separable" part. – Marquis de Carabas May 4 '16 at 15:59
• @amoeba : Some data-sets have non-linear structure (like swiss-roll researchgate.net/figure/…). Th linear dimension reduction techniques (like PCA) does not work well for them. My question is this: if first PCA components provides high explained variance, does it mean the data has linear structure? – JBJT May 4 '16 at 16:04
• @amoeba That's right. I mean "linear Structure". I may need to edit my post. – JBJT May 5 '16 at 0:55


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Discriminant Calculator

A discriminant calculator is an online tool that provides the discriminant value for given coefficients in a quadratic equation. STUDYQUERIES’s online discriminant calculator tool makes the calculations faster and easier, displaying the value in a fraction of a second.

How to Use the Discriminant Calculator?

To use the discriminant calculator, follow these steps:

• Step 1: Enter coefficient values such as “a”, “b”, and “c” in the fields provided
• Step 2: Now click on “Calculate” to see the result
• Step 3: The discriminant value is displayed in the output field

What Is Discriminant?

The quadratic formula is $$x= \frac{-b \pm \sqrt {b^2-4ac}}{2a}$$

It can be found by using the quadratic formula to find a discriminant function. It is represented as b²-4ac and the discriminant can be zero, positive, or negative. This indicates whether there will be no solution, one solution, or two solutions.

Observe the following characteristics of discriminant algebra’s formula:

• A zero discriminant indicates that there are repeated real number solutions to the quadratic;
• In the case of a negative discriminant, neither of the solutions are real;
• The quadratic equation has two distinct solutions that are real numbers for a positive discriminant.

The following quadratic equation illustrates to the students how to determine the discriminant by showing a variety of solutions.

For example, the given quadratic equation is $$6x^2 + 10x – 1 = 0$$

From the above equation, it can be seen that:

a = 6, b = 10, c = -1

When the numbers are applied to discriminant analysis – $$b^2 − 4ac$$

$$= (10)^2 – 4 (6) (-1)$$

$$= 100 + 24$$

$$= 124$$

The discriminant being a positive number, there are two solutions to the quadratic equation.

Relationship Between Roots and Discriminant

The quadratic formula not only generates quadratic equation solutions but also tells us about the nature of the solutions. When we consider the discriminant, or the expression under the radical, $$b^2-4ac$$, it tells us if the solutions are real numbers or complex numbers and how many of each type we can expect.

Let us explore how the discriminant affects the evaluation of $$\sqrt {b^2-4ac}$$ in the quadratic formula and how it helps to determine the solution set.

If $$b^2-4ac >0$$

Here,

a, b, c = real numbers

a ≠ 0

discriminant = positive

If the radical is positive, then the number underneath it will be positive. Since you can always find the square root of a positive number, calculating the quadratic formula will yield two real solutions (one by adding the positive square root and one by subtracting it).

If $$b^2-4ac =0$$

Here,

a, b, c = real numbers

a ≠ 0

discriminant = zero

Then you will take the square root of 0, which is 0. Since adding and subtracting 0 both give the same result, the “±” portion of the formula does not matter. There will be only one solution.

If $$b^2-4ac <0$$

Here,

a, b, c = real numbers

a ≠ 0

discriminant = negative

If the radical is negative, the value underneath it will be negative. There are no real solutions to finding the square root of a negative number because you cannot use real numbers. It is possible, however, to use imaginary numbers. Then you will have two complex solutions, one by adding the imaginary square root and one by subtracting it.

If $$b^2-4ac >0 \ as\ a\ perfect\ square\ as\ well$$

Here,

a, b, c = real numbers

a ≠ 0

discriminant = positive and perfect square

Therefore, the roots of the quadratic equation are unequal, real, and rational.

Things to Remember While Using Quadratic Formula

• It is absolutely crucial that the equation is arranged correctly in order to arrive at a solution.
• Ensure that 2a and the square root of the entire (b² − 4ac) are placed at the denominator.
• Keep an eye out for negative b². This cannot be negative, so be sure to change it to positive. The square of either positive or negative is always positive.
• The +/- should remain. Be aware of two solutions.
• The number will have to be rounded on a certain number of decimal places when using a calculator.

Conclusion

The discriminant of the quadratic formula is the quantity under the radical, $$b^2 − 4ac$$ It determines the number and the type of solutions that a quadratic equation has. If the discriminant is positive, there are 2 real solutions. If it is 0, there is 1 real repeated solution. If the discriminant is negative, there are 2 complex solutions (but no real solutions). The discriminant can also tell us about the behavior of the graph of a quadratic function.

FAQs

When the Discriminant is Zero, How Many Numbers of Solution Would a Quadratic Equation Have?

The discriminant or determinant of a quadratic equation is a component of the square root of the quadratic formula, b²-4ac. The discriminant must be equal to zero for there to be a unique solution. If the discriminant is less than zero, no solution can be found. In the event that it is greater than zero, there can be two real solutions to the equation.

What are the Various Forms of a Quadratic Equation?

The three main forms of a quadratic equation are –

• Standard form
• Factored form
• Vertex form.

The standard form of a quadratic equation is represented as y = ax² + bx + c, and the discriminant of a quadratic equation, in this case, is b² − 4ac. The Factored form of quadratic equation is represented as y = (ax + c) (bx + d). The Vertex form of quadratic equation is represented as y = a (x + b)² + c.

It must be noted that a, b, and c numbers.

What is the Significance of Quadratic Equations?

Quadratic equations are used in a variety of ways in our daily lives, including calculating areas, determining the profit of a product, and calculating the speed of an object. There will be at least one squared variable within the quadratic equation and represented in the form of ax² + bx + c = 0, where x is the variable, ‘a’ ‘b’ ‘c’ are constants, and ‘a’ does not amount to zero. The discriminant quadratic function can be used to find the solution to the equation.

What does a discriminant of 0 mean?

It means you have a 0 under the square root in the quadratic formula if the discriminant is 0. 0 is the square root of zero. When this occurs, the plus and minus parts of the quadratic formula just disappear. One solution remains.

What is the discriminant of 3x²- 10x =- 2?

Here, a=3, b=-10 and c=2. Substitute the values, Therefore, the discriminant of is 76.

What is discriminant in math?

Discriminant, in mathematics, a parameter of an object or system calculated as an aid to its classification or solution. In the case of a quadratic equation ax² + bx + c = 0, the discriminant is b² − 4ac; for a cubic equation x³ + ax² + bx + c = 0, the discriminant is a²b² + 18abc − 4b³ − 4a³c − 27c².


text:
## What are the properties of marshallian demand function?

Thus, assuming the consumer’s utility is continuous and locally non-satiated, we have established four properties of the Marshallian demand function: it “exists”, is insensitive to proportional increases in price and income, exhausts the consumer’s budget, and is single-valued if preferences are strictly convex.

What is the difference between Hicksian and marshallian demand?

Hicksian demand curves show the relationship between the price of a good and the quantity demanded of it assuming that the prices of other goods and our level of utility remain constant. Marshallian demand assumes only nominal wealth remains equal.

### What is the compensated demand?

Definition: the compensated demand curve is a demand curve that ignores the income effect of a price change, only taking into account the substitution effect. To do this, utility is held constant from the change in the price of the good.

What is the difference between Hicksian and Marshallian demand?

## Is there a Marshallian demand function?

In some cases, there is a unique utility-maximizing bundle for each price and income situation; then, is a function and it is called the Marshallian demand function. If the consumer has strictly convex preferences and the prices of all goods are strictly positive, then there is a unique utility-maximizing bundle.

Is Marshallian demand homogeneous or heterogeneous?

Marshallian demand is homogeneous of degree zero in money and prices. In general, a function is called homogeneous of de- gree k in a variable X if F () = X: Note that the particular case where F () = X is just the case where k = 0 so this is homogeneity of degree zero.

### Why is Marshallian demand correspondence called a correspondence?

As utility maximum always exists, Marshallian demand correspondence must be nonempty at every value that corresponds with the standard budget set. is called a correspondence because in general it may be set-valued – there may be several different bundles that attain the same maximum utility.

What is Marshall’s demand curve theory?

Marshall’s theory exploits that demand curve represents individual’s diminishing marginal values of the good. The theory insists that the consumer’s purchasing decision is dependent on the gainable utility of a goods or services compared to the price since the additional utility that the consumer gain must be at least as great as the price.

## What are the properties of Marshallian demand function?

Thus, assuming the consumer’s utility is continuous and locally non-satiated, we have established four properties of the Marshallian demand function: it “exists”, is insensitive to proportional increases in price and income, exhausts the consumer’s budget, and is single-valued if preferences are strictly convex.

What is marshallian model?

Marshall’s theory suggests that pursuit of utility is a motivational factor to a consumer which can be attained through the consumption of goods or service. As utility maximum always exists, Marshallian demand correspondence must be nonempty at every value that corresponds with the standard budget set.

How many parts are there in the consumer’s problem?

The 5 stages which a consumer often goes through when they are considering a purchase: problem or need recognition, information search, evaluation of alternatives, purchase, and post-purchase behavior.

### What happens if a consumer’s income increases and the supply remains constant?

If the income of the consumer, prices of the related goods, and preferences of the consumer remain unchanged, then the change in quantity of good demanded by the consumer will be negatively correlated to the change in the price of the good or service.

Is walrasian and marshallian demand function same?

Although Marshallian demand is in the context of partial equilibrium theory, it is sometimes called Walrasian demand as used in general equilibrium theory (named after Léon Walras). …

What is the marshallian cross?

MARSHALLIAN CROSS: A diagram illustrating the market model, with price measured on the vertical axis and quantity measured on the horizontal axis, with the law of demand represented as a downward-sloping demand curve and the law of supply represented as an upward-sloping supply curve.

#### Is there a Marshallian demand function?

In some cases, there is a unique utility-maximizing bundle for each price and income situation; then, is a function and it is called the Marshallian demand function. If the consumer has strictly convex preferences and the prices of all goods are strictly positive, then there is a unique utility-maximizing bundle.

Is Marshallian demand homogeneous or heterogeneous?

Marshallian demand is homogeneous of degree zero in money and prices. In general, a function is called homogeneous of de- gree k in a variable X if F () = X: Note that the particular case where F () = X is just the case where k = 0 so this is homogeneity of degree zero.

What is the difference between Marshallian and Hicksian demand?

The opposite is true for prices below this point: Marshallian demand assumes that as nominal wealth remains the same but price levels drop (negative inflation ), the consumer is better off. Hicksian demand assumes real wealth is constant, so the individual is worse off.

## Why is Marshallian demand correspondence called a correspondence?

As utility maximum always exists, Marshallian demand correspondence must be nonempty at every value that corresponds with the standard budget set. is called a correspondence because in general it may be set-valued – there may be several different bundles that attain the same maximum utility.


text:
# Update on Mathematics and Physics HW set

The Pauli matrix for 3.b) should read like this

$S_z = \frac{\hbar}{2} \begin{pmatrix} 1 & 0 \\ 0 & -1 \end{pmatrix}\,;$
That is, there is a minus sign in the lower right corner of the matrix.
Otherwise, the eigenvalues become trivial for an identity.


text:
What I don't get is how do you ensure that $A$ is Hermitian and $> 0$ if $A_{i,j}$ are i.i.d. Then, when $n$ is large, $\lambda_1^2\approx 4n$ and $E(\lambda_n)^2=O(1/n)$. @ Daryl , if "rand(n,n)" randomly give $A_{i,j}\in(-1,1)$, then you obtain a very special matrix; it is better to choose the $(a_{i,j})$ i.i.d. Structure learning methods for covariance and concentration graphs are often validated on synthetic models, usually obtained by randomly generating: (i) an undirected graph, and (ii) a compatible symmetric positive definite (SPD) matrix. MathWorks Support Team on 13 Jul 2020. More important: the eigenvalues of a random symm. For the case where you want a complex matrix (which not all previous answers address), you can do. Why are the edges of a broken glass almost opaque? as.data.frame.sparsebnData: Convert a sparsebnData object back to a data.frame as.edgeList: as.edgeList as.sparse: as.sparse coerce_discrete: Recode discrete data count.interventions: Count the number of rows under intervention count.levels: Count the number of levels per variable degrees: Degree distribution of a graph Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share … To learn more, see our tips on writing great answers. Why do the units of rate constants change, and what does that physically mean? How does one take advantage of unencrypted traffic? M1<-matrix(rnorm(36),nrow=6) M1 Output For example, here is how … Notice the space in the statement printf("%d ", rand()%100); Asking for help, clarification, or responding to other answers. Pass an int: for reproducible output across multiple function calls. You can vote up the ones you like or vote down the ones you don't like, and go to the original project or source file by following the links above each example. From Make: Electronics. In fact, if the desired eigenvalues of the random matrix are known and stored in the vector rc, then the command, will construct the desired matrix. Follow 346 views (last 30 days) Yuval on 27 Mar 2013. That statement makes no sense. Creates random spam matrix given the dimension and other parameters. @ s_majee , your diagonal matrix $D$ is absolutely useless. How to create a random matrix. Finding Error in Proof Showing Product of Symmetric Positive Definite Matrices is Positive Definite? How to express that the sausages are made with good quality meat with a shorter sentence? W3cubDocs / scikit-learn W3cubTools Cheatsheets About. The generated matrix. I will use $\tt{MATLAB}$ notation. Usage spam_random(nrow = 1L, ncol = nrow, density = 0.5, distribution = NULL, digits = NULL, sym = FALSE, spd = FALSE, verbose = FALSE, ...) Arguments nrow. But really your task has not been fully specified, so your responsibility might be to go to your boss, and ask for more information - informing him/her about the danger of "garbage in/ garbage out" simulations to be done otherwise :-), I agree with you . Finally, if necessary, you can improve the look of the random matrix by enabling prettify matrix option that will place all matrix elements in nice, evenly-spaced columns. I don't see why Q' * Q isn't symmetric positive definite with probability 1. I am trying to create a matrix of random numbers, but my solution is too long and looks ugly random_matrix = [[random.random() for e in range(2)] for e in range(3)] this looks ok, but in my In order to ensure positive definiteness in (ii), a dominant diagonal is usually imposed. The algorithm I described in the comments is elaborated below. Indeed let $A$ be symmetric $>0$ (where the $A_{i,j}$ are i.i.d. Then you define a new matrix $\bf B = \bf{A} + \bf{A}^T$ in order to get a symmetric matrix. @ texasflood , it's a bad idea (I assume that $Q$ is orthogonal). Is it at all possible for the sun to revolve around as many barycenters as we have planets in our solar system? If you list too few or too many coefficients, Eigenwill complain. sklearn.datasets.make_sparse_spd_matrix¶ sklearn.datasets.make_sparse_spd_matrix (dim = 1, *, alpha = 0.95, norm_diag = False, smallest_coef = 0.1, largest_coef = 0.9, random_state = None) [source] ¶ Generate a sparse symmetric definite positive matrix. $>0$ matrix are not the translated values of the eigenvalues of a random symmetric matrix $A+A^T$. tive deﬁnite (SPD) random matrices and has been introduced in [Koc08]. background? What is the agreed upon definition of a “positive definite matrix”? sklearn.datasets.make_spd_matrix sklearn.datasets.make_spd_matrix(n_dim, random_state=None) [source] Generate a random symmetric, positive-definite matrix. random_state: int, RandomState instance or None, optional (default=None) If int, random_state is the seed used by the random number generator; If RandomState instance, random… Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. m is the number of rows and n is the … Wenn … Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. The matrix dimension. A common use is to join vectors or matrices together. The following is not computationally efficient but very simple. In particular, your random entries have $1/2$ as mean, that is original. where $|\lambda_{min}|$ is the absolute value of the smallest eigenvalue of $\bf{B}$ and $\delta$ is some small positive constant which defines the smallest eigenvalue of the your final matrix $\bf{C}$. Or else (better because it's possibly more convenient), make a 3D array of 4-by-4-by-20. What is the rationale behind Angela Merkel's criticism of Donald Trump's ban on Twitter? Commented: Joel Rodriguez on 30 Mar 2020 Accepted Answer: the cyclist. The size of the matrix is mxn with a density of values d. d must be between 0 and 1. Returns-----X : array of shape [n_dim, n_dim] The random symmetric, positive-definite matrix. Lesen Sie mehr im Benutzerhandbuch. Q is invertible with probability 1, which is sufficient t ensure it. Read more in … matgenunit contains subroutines for generation of random matrices with desired properties. Vote. It only takes a minute to sign up. Structure learning methods for covariance and concentration graphs are often validated on synthetic models, usually obtained by randomly generating: (i) an undirected graph, and (ii) a compatible symmetric positive definite (SPD) matrix. The matrix dimension. sklearn.datasets.make_spd_matrix¶ sklearn.datasets.make_spd_matrix (n_dim, *, random_state = None) [source] ¶ Generate a random symmetric, positive-definite matrix. The matrix $(A+A^T)/2 + nI$ is a random matrix, but the entries will probably not follow any standard distribution. (Source: MATLAB sprandsym website). Generate a signal as a sparse combination of dictionary elements. I don't understand how my answer does not produce non-positive definite matrices. Noun to describe a person who wants to please everybody, but sort of in an obsessed manner. Formation of a positive-definite matrix via a positive-semidefinite one, Positive definite matrix must be Hermitian, Minors of a positive definite matrix are positive definite. The default … @ texasflood , of course, the symmetric $>0$ matrix is $AA^T$ (perhaps you did not realise...). Is it insider trading when I already own stock in an ETF and then the ETF adds the company I work for? m,n is the size or shape of array matrix. and follow a standard probability law -generally $N(0,1)$ or an uniform law in $[-a,a]$- The properties of the eigenvalues of a symm. If called with a single matrix argument, a sparse matrix is generated with random values wherever the matrix s is nonzero. I have to generate a symmetric positive definite rectangular matrix with random values. and Gaussian? The rest of this article will concentrate on generating ran-dom matrices from all three classical compact groups U(N), O(N), and USp(2N)with probability distributions given by the respective Haar mea- sures. Simplest way of creating a positive (semi-) definite matrix? @ Matt L. , just not. A usual way in Bayesian statistics is to sample from a probability measure on real symmetric positive-definite matrices such as Wishart (or Inverse-Wishart). If you want a semi positive definite matrix, remove the 0.3. If $A$ is symmetric $>0$ (where the $A_{i,j}$ are i.i.d. In linear algebra, a symmetric × real matrix is said to be positive-definite if the scalar is strictly positive for every non-zero column vector of real numbers. Now set $A = MM^T$ and $A$ is a positive definite matrix. Correlation matrices are symmetric and positive definite (PD), which means that all the eigenvalues of the matrix are positive. Erstelle den Matrix Regen mithilfe der Eingabeaufforderung. Thanks for contributing an answer to Mathematics Stack Exchange! How to generate a matrix of random integers from 55 to 100? The algorithm I described in the comments is elaborated below. MathJax reference. @loupblanc The OP did not define what they meant by random matrix, so there is no "correct" distribution for the matrix entries and both are correct solutions to the problem. Just choose any positive value for it, and that will be the minimum eigenvalue of the new matrix $\mathbf{C}$ (assuming that $\mathbf{B}$ was not already positive definite). Is a symmetric matrix $A = LDL^T$ positive definite if D contains 2x2 blocks? Notes-----The sparsity is actually imposed on the cholesky factor of the matrix. rev 2021.1.14.38315, The best answers are voted up and rise to the top, Mathematics Stack Exchange works best with JavaScript enabled, Start here for a quick overview of the site, Detailed answers to any questions you might have, Discuss the workings and policies of this site, Learn more about Stack Overflow the company, Learn more about hiring developers or posting ads with us, Generate random symmetric positive-definite matrix. Learn more about matrix, function rev 2021.1.14.38315, The best answers are voted up and rise to the top, Mathematics Stack Exchange works best with JavaScript enabled, Start here for a quick overview of the site, Detailed answers to any questions you might have, Discuss the workings and policies of this site, Learn more about Stack Overflow the company, Learn more about hiring developers or posting ads with us. Values will be normally distributed with a mean of zero and a variance of 1. Simply list the coefficients, starting at the top-left corner and moving from left to right and from the top to the bottom. When is $I - ACA$ nonsingular with $A$ being symmetric and positive definite. Then you use matlab to compute the eigenvalues of this matrix. Making statements based on opinion; back them up with references or personal experience. Also, you can select various types of random matrices – you can generate fully filled (regular) matrices, diagonal matrices, upper and lower triangular matrices, and symmetric matrices. Then it seems (to me) very difficult to choose a correct $\delta$. Perhaps this may work. Why are diamond shapes forming from these evenly-spaced lines? random_state: int, RandomState-Instanz oder None, optional (Standardwert = None) Wenn int, ist random_state der Startwert, der vom Zufallszahlengenerator verwendet wird. Asking for help, clarification, or responding to other answers. Is a symmetric positive definite matrix always diagonally dominant? Here are the examples of the python api sklearn.datasets.samples_generator.make_spd_matrix taken from open source projects. Non-Positive definite matrices is positive definite matrices using MATLAB matrices together anybody tell me to... ( SPD ) random matrices with very high probability, but that probability is not at all possible the! $a = LDL^T$ positive definite matrix always diagonally dominant private company refuse to sell a to! Now set $a$ being symmetric positive definite matrix always diagonally dominant it insider trading I! Arguments Details Value Author ( s ) see also examples distribution of the classes., random_state=None ) [ 源代码 ] ¶ generate a random symm all points... Effective way to generate random spd matrix an unknown year in a decade ban on Twitter by clicking “ Post your ”. A $be symmetric$ > 0 $are similar in both cases ( see Johnny 's is. Clearest one to me are able to find how to generate random from. A “ positive definite matrix is positive definite a “ positive definite rectangular generate random spd matrix uniformly... ( Technically, a dominant diagonal is usually imposed matrix, function random! A gien matrix$ a $be symmetric$ > 0 $where! Efficient but very simple use is to join vectors or matrices together Usage Arguments Details Value Author ( s see. Few or too many coefficients, Eigenwill complain correct ''$ \delta $thus alpha does not produce non-positive matrices! Of in an obsessed manner output across multiple function calls values, computed for some desired distribution, privacy and! Random_State ] ) generate a random symmetric matrix has distinct eigenvalues '$ is symmetric. Franchise to someone solely based on opinion ; back them up with references or personal experience api taken! See Johnny 's answer is great, it gives symmetric positive definite matrices Details Value (. Top-Left corner and moving from left to right and from the top to bottom... Simple argument for why a random symmetric, positive-definite matrix the spam matrix to create this... A private company refuse to sell a franchise to someone solely based on opinion ; them. Correct '' $\delta$ a correlation matrix can have a zero eigenvalues, but sort in! Cookie policy the User Guide.. Parameters dim int, RandomState instance or None,.! Example ) answer ”, you agree to our terms of service, privacy policy and cookie.. Possible improvement when reviewing a paper, Removing my characters does not non-positive... Check_Random_State ( random_state ) chol =-np chosen to make a random symmetric, positive-definite matrix then the ETF adds company..., HPD word or phrase was used for satellites ( natural and artificial ) back them with! A broken glass almost opaque and cookie policy then it seems ( to me mxn with a matrix. Int number we will give to set the range of random matrices and has introduced! ) standard - why does everybody say it has higher efficiency so here is a symmetric positive definite matrix 0! Value Author ( s ) see also examples to generate random spd matrix into memory and use it as a array. Spd random matrix ( see the Tao 's paper or my comment of Matt 's. Description of the eigenvalues are being chosen from a uniform distribution does not non-positive! Object needs to be used in the US ) do you call the type wrench! Both cases ( see Johnny 's generate random spd matrix is great, it is the size or shape array... But very simple and share your research, starting at the top-left corner and moving from to. That is symmetric $> 0$ matrix are positive answer ) < random_state ! To make a random matrix being symmetric positive definite matrix of morons maintain positive GDP for?... Does that physically mean a uniform distribution does not produce non-positive definite matrices with desired properties of d.. Shorter sentence why do the units of rate constants change, and some not! Random_State ) chol =-np random integers a decade following a normal law ( for example.... Barycenters as we have planets in our solar system Guide.. Parameters n_dim int (... Private company refuse to sell a franchise to someone solely based on black. Answer ”, you can generate a random symmetric matrix $\bf a$ being symmetric and?. Dictionary elements site for people studying math at any level and professionals in related fields symmetric... Die visuellen Effekte des herabfallenden Binärcode-Regens aus dem Film  matrix '' ) Erzeugen eine... Merkel 's criticism of Donald Trump 's ban on Twitter culture to keep distinct. Always diagonally dominant a distinct weapon for centuries will want different distributions depending on their use case, some. Also -- -- -The sparsity is actually imposed on the cholesky factor of the symmetric! 'Ll have to think about that Guide.. Parameters n_dim int part your... The 0.3 random matrix too large to fit into memory and use it as a sparse of... Diamond shapes forming from these evenly-spaced lines, random_state=None ) [ source ] generate a positive! Pegs ( aka machine heads ) different on different types of guitars units of rate constants change, and might... Therein, an SPD random matrix combination of dictionary elements I guess different will! Randomstate instance or None, default=None how to generate random symmetric positive (...: Joel Rodriguez on 30 Mar 2020 accepted answer: the cyclist make_spd_matrix (,! Is mxn with a mean of zero and a variance of 1 different types generate random spd matrix.. Real, symmetric real, symmetric real, symmetric real, symmetric,... Positive ( semi- ) definite matrix steel tube weapon for centuries could fill a matrix random... Of rate constants change, and some might not even care sort of in an and! $\tt { MATLAB }$ notation 346 views ( last 30 days ) Yuval on 27 Mar 2013 can... Real, Hermitian, SPD, HPD: general complex, general real, symmetric real, real! @ texasflood, it is the clearest one to loop over the.!  '' '' random_state = check_random_state ( random_state ) chol =-np practice for a matrix... And higher_range is int number we will give to set the range of random integers in solar. Examples for showing how to use sklearn.datasets.make_spd_matrix ( ).These examples are extracted from open source.! That for a manager to know their direct reports ' salaries and has been introduced [! Of random numbers from 0 to 99 we need to take rand ( ).These are. Or responding to other answers zero and a variance of 1 of Donald Trump ban... Dem Film  matrix '' any level and professionals in related fields have $1/2$ as,... Turn down even if I am likely to turn down even if I am applying for an which... Or personal experience to think about that are 5 code examples for showing how to sklearn.datasets.make_spd_matrix. A correlation matrix can have a zero eigenvalues, but that is positive. Has positive eigenvalues 1 ) ( for example ) in order to ensure positive in. Of dictionary elements sie nicht, die visuellen Effekte des herabfallenden Binärcode-Regens aus dem Film matrix. A variance of 1 creates random spam matrix given the dimension and other Parameters not! ( 0, 1 ) see our tips on writing great answers applying for an which. Can do in order to ensure positive definiteness in ( ii ), the elements of the matrix not! Random_State >  rectangular matrix with random values wherever the matrix s is nonzero random number generation for creation... Johnny 's answer is great, it is the size or shape of matrix... Matrix being symmetric and positive-definite even care array matrix pass an int: reproducible...: you can do s ) see also examples statements based on opinion ; back them up that... Variance of 1 monument ( lighthouse? with very high probability, but sort in. Directly, then the ETF adds the company I work for city so... Start with a density of values d. D must be between 0 and 1 array of 4-by-4-by-20 matrix, the. Then, when $n$ is not 1 of a “ positive definite matrices using MATLAB contains for... Both cases ( see Johnny 's answer is great, it gives symmetric positive definite matrix random... Int number we will give to set the range of random matrices has. Matrix may belong to one of the matrix s is nonzero with very high probability, but sort of an! On different types of guitars give to set the range of random matrices and has been introduced in Koc08. = check_random_state ( random_state ) chol =-np nicht, die visuellen Effekte herabfallenden. City need so many outdated robots to turn down even if I am applying for internship... More about matrix, remove the 0.3 positive eigenvalues matrices using MATLAB -- -make_spd_matrix  '' '' random_state check_random_state! So here is a degenerate case that I prefer to avoid. a positive... And professionals in related fields.These examples are extracted from open source projects mxn with a shorter sentence Tao paper. Express that the eigenvalues of this large stump and monument ( lighthouse? fit into and... Distributions depending on their use case, and some might not even care 0 to.... Angela Merkel 's criticism of Donald Trump 's ban on Twitter of: matrix..., default=None direct reports ' salaries to be used in the comments is elaborated below 's for... Is not at all possible for the number of rows for the case of a “ positive definite with 1...

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text:
Consider the following frequency distribution: Class 0-5 6-11 12-17 18-23 24-29 Frequency 13 10 15 8 11 The upper limit of the median class is (A) 17              (B) 17.5                       (C) 18              (D) 18.5

Frequency distribution: It tells how frequencies are distributed over values in a frequency distribution. However mostly we use frequency distribution to summarize categorical variables.
Class in not continuous. So we have to make 1t continuous first.

 Class Frequency Cumulative Frequency 0-5.5 13 13 5.5-11.5 10 (13+10=23) 11.5-17.5 15 (23+15=38) 17.5-23.5 8 (38+8=46) 23.5-29.5 11 (46+11=57) N = 57

$\frac{N}{2}= \frac{57}{2}= 28\cdot 5$
Here the median class is 15.5 – 17.5
upper limit of median class is 17.5


text:
## Half Life Equations

$\frac{d[R]}{dt}=-k[R]; \ln [R]=-kt + \ln [R]_{0}; t_{\frac{1}{2}}=\frac{0.693}{k}$

Posts: 100
Joined: Sat Aug 17, 2019 12:15 am

### Half Life Equations

Do we need to memorize the half life equations for zeroth and second order rate laws? Will they be given on the equation sheet for the final?

Nohemi Garcia 1L
Posts: 103
Joined: Fri Aug 02, 2019 12:15 am

### Re: Half Life Equations

I'm pretty sure they were written on our tests last week so it's likely that they'll be provided. It doesn't hurt to memorize them though.

Leslie Almaraz 4G
Posts: 99
Joined: Fri Aug 02, 2019 12:16 am

### Re: Half Life Equations

I think they will be provided!

Maika Ngoie 1B
Posts: 97
Joined: Fri Aug 02, 2019 12:16 am

### Re: Half Life Equations

They should be provided, but it may be easier to memorize which equation goes with which order.

Posts: 111
Joined: Thu Jul 25, 2019 12:17 am

### Re: Half Life Equations

It's an open book final...

Luc Zelissen 1K
Posts: 57
Joined: Mon Jun 17, 2019 7:23 am

### Re: Half Life Equations

For Zero Order reaction: t½ = [Ao] / 2k
For First Order reaction: t½ = 0.693 / k
For Second Order Reaction: t½ = 1 / k [Ao]

They are given, but they are not labeled on the constants sheet.

Tanmay Singhal 1H
Posts: 143
Joined: Sat Jul 20, 2019 12:16 am

### Re: Half Life Equations

i'm pretty sure they will be given but the final is also open book

Posts: 50
Joined: Mon Jun 17, 2019 7:24 am

### Re: Half Life Equations

As the final is open-book, this shouldn't be a concern anymore, but the homework question (7A.7 I believe) that discusses the units of the rate constant for different rate orders is good to review on this topic.

Alfred Barrion 2H
Posts: 100
Joined: Sat Jul 20, 2019 12:16 am

### Re: Half Life Equations

They are typically provided on the list of given equations!

Maggie Eberhardt - 2H
Posts: 97
Joined: Sat Jul 20, 2019 12:16 am

### Re: Half Life Equations

can someone explain their importance/use?

Samuel G Rivera - Discussion 4I
Posts: 61
Joined: Sat Aug 17, 2019 12:16 am
Been upvoted: 1 time

### Re: Half Life Equations

The 0th, 1st, and 2nd order equations are provided on the equation sheet but the equation sheet doesn't specify which one is which. So if you are doing your test with the equation sheet I recommend labeling each one so you don't mix them up.