Core course for B.Sc. (Research) Mathematics.
Credits (Lec:Tut:Lab)= 3:1:0 (3 lectures and 1 tutorial weekly)
Prerequisites: Class XII Mathematics
Overview: Linear Algebra provides the means for studying several quantities simultaneously. A good understanding of Linear Algebra is essential in almost every area of higher mathematics, and especially in applied mathematics. A CAS such as Maxima/Matlab will be used throughout the course for computational purposes.
- Matrices and Linear Systems
- Vector Spaces and Linear Transformations
- Inner Product Spaces
- Eigenvalues and Eigenvectors, Diagonalization
- Quadratic Forms and Positive Definite Matrices
- Applications chosen from: Numerical aspects, Difference equations, Markov matrices, Least squares.
- Linear Algebra by Jim Hefferon
- Linear Algebra and its Applications by Gilbert Strang, 4th edition, Cengage.
- Linear Algebra and its Applications by David C. Lay, 3rd edition, Pearson.
- Linear Algebra: A Geometric Approach by S. Kumaresan, PHI, 2011.
- Elementary Linear Algebra by Howard Anton and Chris Rorres, 9th edition, Wiley.
- Linear Algebra: An Introductory Approach by Charles Curtis, Springer.
- Matrix Analysis and Applied Linear Algebra by Carl D Meyer, SIAM.
- Videos of lectures by Prof Gilbert Strang: 18.06 Linear Algebra, Spring 2010. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu