Linear Algebra

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.

Detailed Syllabus:

1. Matrices and Linear Systems
2. Vector Spaces and Linear Transformations
3. Inner Product Spaces
4. Determinant
5. Eigenvalues and Eigenvectors, Diagonalization
6. Quadratic Forms and Positive Definite Matrices
7. Applications chosen from: Numerical aspects, Difference equations, Markov matrices, Least squares.

References:

1. Linear Algebra by Jim Hefferon
2. Linear Algebra and its Applications by Gilbert Strang, 4^th edition, Cengage.
3. Linear Algebra and its Applications by David C. Lay, 3^rd edition, Pearson.
4. Linear Algebra: A Geometric Approach by S. Kumaresan, PHI, 2011.
5. Elementary Linear Algebra by Howard Anton and Chris Rorres, 9^th edition, Wiley.
6. Linear Algebra: An Introductory Approach by Charles Curtis, Springer.
7. Matrix Analysis and Applied Linear Algebra by Carl D Meyer, SIAM.
8. Videos of lectures by Prof Gilbert Strang: 18.06 Linear Algebra, Spring 2010. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu