# Tagged Questions

The linear-algebra tag has no wiki summary.

0answers
38 views

### how to represent Sparse Matrices

I have been using Harwell Boeing format, also known as Compressed Column Strorage (CCS) in order to store Sparse Matrices. Could you please suggest me some other way to store/represent sparse ...
2answers
62 views

### Finding the required value of an algebric expression

I have an expression $$Ax+By+Cz.$$ where $A$, $B$ and $C$ are positive constants $\ge1$. The variables $x$, $y$ and $z$ are non-negative integers. I am also given a number $T$. I want to find the ...
3answers
30 views

### Solving system of linear inequalities

I am trying to solve a system of inequalities in the following form: $\ x_i - x_j \leq w$ I know these inequalities can be solved using Bellman-Ford algorithm. ...
2answers
78 views

### Can you complete a basis in polynomial time?

Here is the problem: we are given vectors $v_1, \ldots, v_k$ lying in $\mathbb{R}^n$ which are orthogonal. We assume that the entries of $v_i$ are rational, with numerator and denominator taking $K$ ...
1answer
41 views

### Counting solutions to system of linear equations modulo prime

I have implemented Gaussian elimination for solving system of linear equations in the field of modulo prime remainders. If there is a pivot equal to zero I assume the system has no solution but how to ...
2answers
95 views

### What is the complexity of this matrix transposition?

I'm working on some exercises regarding graph theory and complexity. Now I'm asked to give an algorithm that computes a transposed graph of $G$, $G^T$ given the adjacency matrix of $G$. So basically ...
0answers
28 views

### multigrid method to solve PDE [closed]

I need explanation of the Multigrid Method or some literature. I am familiar with iterational methods including BiCGStab,CG,GS,Jacobi and preconditioning, but I am a beginner with multigrid method. ...
1answer
46 views

### LU decomposition with pivoting

I have to solve system of linear algebraic equations $AX=B$, where $A$ is a two-dimensional matrix with all elements of main diagonal equal to zero. How to solve this problem? Iterational methods are ...
1answer
121 views

### Machine Learning: how to correctly calculate gradient descent for simple linear problem

So, I was trying to learn machine learning, and, after watching a couple of Andrew Ng's lectures decided to try and write a simple piece of code to determine what someone's salary would be based on ...
0answers
22 views

### Maximum feasible subsystem problem (MaxFS) in 2 variables

Topic: The maximum feasible subsystem problem, which is generally NP-hard [1]. Question: Are there special algorithms in case of only 2 variables (2D linear constraints)? The problem seems to be a ...
0answers
103 views

### Alternatives to SVD for rank factorization

I have rank-deficient matrix $M \in \mathbb{R}^{n\times m}$ with $\text{rank}(M) = k$ and I want to find a rank factorization $M = PQ$ with $P \in \mathbb{R}^{n \times k}$ and \$Q \in \mathbb{R}^{k ...
0answers
40 views

### Time - Complexity Convex Optimization and Eigen Decomposition

Say I had the choice of choosing one out of the following two optimization problems which I could use to solve my problem. Which choice is the fastest? How much of a trade-off would it be? Is the ...
1answer
117 views

### Probabilistic test of matrix multiplication with one-sided error

Given three matrices $A, B,C \in \mathbb{Z}^{n \times n}$ we want to test whether $AB \neq C$. Assume that the arithmetic operations $+$ and $-$ take constant time when applied to numbers from ...
1answer
352 views

### Complexity of checking whether linear equations have a positive solution

Consider a system of linear equations $Ax=0$, where $A$ is a $n\times n$ matrix with rational entries. Assume that the rank of $A$ is $<n$. What is the complexiy to check whether it has a solution ...
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