E0 332: Matrix Analysis and Computations

• Announcements:

1. Final exam: 8/12, 10 am - 1 pm.

2. Second mid-term exam: 15/11, 11:30 am - 1:00 pm.

3. Project presentations: 12/12 and 13/12, 10 am - 1 pm.

4. First mid-term exam: 29/9, 11:30 am - 1:30 pm.

5. New venue: B-304 and timing: 11:30 am-1:00 pm.

6. The first meeting is on August 2nd at 10 am.

Course Details

• Term: August - December 2016.

• Credits: 3:1

• Webpage: http://tinyurl.com/course-mac2016

• Venue: B-304 (EE Department).

• Hours: Tuesday and Thursday (11:30 am - 1:00 pm).

• Instructor: Kunal N. Chaudhury (kunal@ee.iisc.ernet.in).

• Prerequisite: Basic linear algebra and calculus.

• Overview: We will look at various analytical aspects of linear algebra, particularly its connection with variational methods. The emphasis will be on understanding fundamental theorems, their proofs, and on their applications. Selected computational topics will be examined through projects and presentations.

• Topics

1. Analysis: Spectral theory of self-adjoint and normal matrices, Courant-Fischer principle, Weyl and Lidskii theorems, interlacing theorems, partial trace, Ky-Fan inequality; calculus of matrix-valued functions, vector and matrix-valued maps, matrix norms, operator norm, convergence; matrix inequalities, function of matrices, inequalities involving trace, norm, eigenvalue and determinant, matrix exponential, Golden-Thompson inequality; Perron-Frobenius theory, positive matrices and Perron's theorem, extension to non-negative matrices, irreducibility, stochastic matrices; diagonalizable matrices, similarity transformations, Schur's theorem, Jordan decomposition.

2. Computation: Projects on various computational topics.

• Course structure: About 28 lectures, problem sets, mini-project, 2 mid-terms, final exam.

• Grading: Mid-terms: 25%, Mini-project: 25% Final exam: 50%.

• References:

1. Bellman, Introduction to Matrix Analysis.

2. Bhatia, Matrix Analysis.

3. Trefthen and Bau, Numerical Linear Algebra.