Math 202A: Applied Algebra I (Matrix Analysis)

Fall 2022

Math 202A. is concerned with the study of linear algebra, with an emphasis on matrix analysis.

Please note that Math 202A is not a class on numerical or computational (linear) algebra. Neither is it an algebra class with examples taken from matrix algebra. The focus of the class is on matrix analysis, which (not surprisingly) involves the study of matrices and their algebraic properties.

Topics (subject to change):

• Structure revealing matrix decompositions

  Schur decomposition, spectral decomposition, Jordan canonical form.

• Eigenvalues, eigenvectors and their characterization

  Field of values, Courant-Fischer theorem, Toeplitz-Hausdorff theorem, eigenvalue interlacing theorems.

• Matrix norms and their properties

  Singular-value decomposition, polar decomposition, unitarily invariant norms, dual norms, gauge theory.

• Matrix perturbation theory

  Cosine-sine decomposition, matrix projection, perturbation of subspaces, Von Neumann trace theorem.

Recommended text:

• Matrix Analysis (2nd Edition), by R. A. Horn and C. R. Johnson, Cambridge University Press, 2013, ISBN 978-0-521-54823-6 (Paperback), 978-0-521-83940-2 (Hardback).

On-line access:

Grading options:

• Letter grade: The grade will be based on a final examination: Monday, December 5th, 11:30a--2:30p
  The final will be an in-person "closed-book" examination based on homework problems assigned during the quarter.
• SU grade: Students need not take the final examination, but must make a "fair attempt" at the homework assignments.