Advanced Linear Algebra (Math 390, Spring 2021)

Course Information


SCLA and FCLA by Beezer;
TB and SW are a close fit to our course's goals;
GVL, HJ and DW are encyclopedic reference works;
HLA is meant to be a comprehensive, encyclopedic resource.

Course Calendar

Course Introduction, Vector Spaces (Tuesday, January 19)
Vector Space Properties (Thursday, January 21)
Linear Transformations (Friday, January 22)
Representations (Monday, January 25)
Problem Session (Tuesday, January 26)
Eigenvalues I (Thursday, January 28)
Eigenvalues II (Friday, January 29)
Invariant Subspaces (Monday, February 1)
Problem Session (Tuesday, February 2)
Similarity and Diagonalization (Thursday, February 4)
Similarity and Diagonalization (Friday, February 5)
Characteristic Polynomial (Monday, February 8)
Problem Session (Tuesday, February 9)
Matrices (Thursday, February 11)
Direct Sums, Orthogonal Complements (Friday, February 12)
Review, Problems (Monday, February 15)
Exam 1 (Tuesday, February 16)
Jordan Canonical Form (Monday, February 22)
Jordan Canonical Form (Tuesday, February 23)
Jordan Canonical Form (Thursday, February 25)
Jordan Canonical Form (Friday, February 26)
Rational Canonical Form (Monday, March 1)
Matrix Decompositions, LU Decomposition (Thursday, March 4)
QR Decomposition (Friday, March 5)
QR Decomposition, Householder Reflectors (Monday, March 8)
Problem Session (Tuesday, March 9)
Householder Reflectors, QR Decomposition (Thursday, March 11)
Normal Matrices, Positive Semi-Definite Matrices, SVD (Friday, March 12)
Positive Semi-Definite Matrices, SVD (Monday, March 15)
Problem Session (Tuesday, March 16)
SVD (Thursday, March 18)
SVD (Friday, March 19)
SVD (Monday, March 22)
Problem Session (Tuesday, March 23)
Orthonormal Diagonalization (Schur Decomposition) (Thursday, March 25)
Orthonormal Diagonalization (Schur Decomposition) (Friday, March 26)
Cholesky Decomposition (Thursday, April 1)
Least Squares (Friday, April 2)
Problem Session (Monday, April 5)
Exam 2 (Tuesday, April 5)
Least Squares (Thursday, April 8)
Least Squares (Friday, April 9)
Projectors (Monday, April 12)
Problem Session (Tuesday, April 13)
Projectors (Thursday, April 15)
Projectors (Friday, April 16)
Determinants with Permutations (Monday, April 19)
Problem Session (Tuesday, April 20)
Determinants with Permutations (Thursday, April 22)
Determinants with Permutations (Friday, April 23)
Determinants via Axioms (Monday, April 26)
Problem Session (Tuesday, April 27)
Presentations (Monday, May 3)
Presentations (Monday, May 4)



Sage is open-source software for advanced mathematics. There are several ways to use it, here are two of the easiest.

Main website for Sage: Sage Website

Presentation Advice

Project Topics

These are simply suggestions. Some I know well, some I know little about. Some are excellent choices, some will be harder than others. And you are not limited to just these topics. Many of these have been done by UPS students before (see Math 420 Spring 2014), so you need to be sure your approach is substantially different.


This is:
Maintained by: Rob Beezer
Last updated: January 20, 2021