Math 202A: Applied Algebra I (Matrix Analysis)
Fall 2022
This is the first part of the graduate Applied Algebra sequence Math
202ABC.
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, CourantFischer theorem, ToeplitzHausdorff theorem, eigenvalue interlacing theorems. 

 Matrix norms and their properties

Singularvalue decomposition, polar decomposition, unitarily invariant norms, dual norms, gauge theory. 

 Matrix perturbation theory

Cosinesine 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 9780521548236 (Paperback), 9780521839402 (Hardback).
Online access:
In addition to this website, the course has a Canvas page that also provides access to Gradescope.
Grading options:
 Letter grade: The grade will be
based on a final examination: Monday, December 5th, 11:30a2:30p
The final will be an inperson "closedbook" 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.
I prefer not to answer technical questions by email ( n emails for me
to understand your question, m emails for you to understand my
answer), but students are welcome to callin via Zoom during my office hours or after
class.
Class location: 
AP&M 2402 
Remote access: 
Synchronous broadcast on Canvas/Zoom. 
Class time: 
MWF 1:00p  1:50p 
Instructor: 
Philip E. Gill 
Office hours: 
See the Canvas Module: Introduction to Math 202A 
TA: 
Ziyan Zhu 
Office hours: 
See the Canvas Module: Introduction to Math 202A 