E0 332: Matrix Analysis


  • Announcements:

  1. The first meeting is on August 2 at 10 am in B-308.

  2. The first mid-term will be on September 27 during class hours.

  3. We will discuss the assignment problems on September 20.

  4. The lecture timing will be 10 - 12 from October 23.

  5. The second mid-term will be on November 29 during class hours.

  6. The final exam is on December 10 from 10am - 1 pm (in B-308).

  7. The final lecture is on November 22.

Course Details

  • Term: August - December 2018.

  • Credits: 3:0.

  • Hours: Tuesday and Thursday (10:00 - 11:30 am).

  • Venue: B-308.

  • Webpage: tinyurl.com/y4kgl7xl

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

  • Prerequisites: Solid knowledge of linear algebra and calculus (mandatory).

  • Scope: We will look at various analytical aspects of linear algebra, particularly its connection with variational methods. The emphasis will be on understanding fundamental theorems and their proofs. This is an advanced course targeted at research students.

  • Course structure: Problem sets, problem solving sessions, two mid-terms, and an exam.

  • Grading: Mid-terms: 50%, Exam: 50%.

  • References:

  1. Bellman, Introduction to Matrix Analysis.

  2. Meyer, Matrix Analysis and Applied Linear Algebra.

  3. Lecture notes (posted below).

  • Notes:

[1] Basic definitions and theorems from linear algebra. [pdf]

[2] Spectral theory of Hermitian matrices, perturbation results. [pdf]

[3] Calculus of matrix-valued functions, matrix exponential. [pdf]

[4] Matrix inequalities involving trace, determinant, and eigenvalues. [pdf]

[5] Davis-Kahan theorem and its application to PCA. [pdf]

[6] General spectral theory and the Jordan form. [pdf]

[7] Positive and non-negative matrices, Perron-Frobenius theory. [pdf]

The main results are discussed in the notes. Detailed proofs will be provided during the lecture.

  • Problem set [pdf].