Dr. Hugo J. Woerdeman
hugo@math.drexel.edu
Korman 206
Office Hours: TBA

Topics in Matrix Analysis
by Roger A. Horn, Charles R. Johnson
(ISBN-13: 9780521467131 | ISBN-10: 0521467136)

This course is a follow up on Math 504: Linear Algebra and Analysis. Central to this course are the following ten theorems, which will be treated along with their background, consequences and applications:

1. Toeplitz-Hausdorff Theorem
2. Ando's characterization of the numerial radius unit ball
3. Lyapunov's Theorem
4. Fischer's Inequality for M-matrices
5. Birkhoff's Theorem
6. A. Horn's Matrix Product Theorem
7. A. Horn's Sufficiency Theorem
8. Solvability Theorem for AX+XB=C
9. Schur Product Theorem
10. Lie Product Formula

The course assumes an advanced knowledge of linear algebra, acquired for instance in Math 504. Assumed background knowledgde includes Schur's Triangularization Theorem, the Jordan Canonical Form, Spectral Theorems for Hermitian and Normal Matrices, The Courant-Fischer Theorem, Interlacing Eigenvalues Theorem, Singular Value Theorem, Perron-Frobenius Theorem.

Matrix Analysis - by Roger Horn and Charles Johnson
The Theory of Matrices - by Peter Lancaster, Miron Tismenetsky
Applied Linear Algebra - by B. Noble, J. Daniel
Linear Algebra - by Kenneth Hoffman, Raymond Kunze
Linear Algebra Done Right - by Sheldon Axler
Linear Algebra - by Stephen Friedberg
Matrix Computations - by Gene Golub, Charles Van Loan
Numerical Linear Algebra - by L. Trefethen, D. Bau
Linear Algebra - by Peter Lax
Matrix Analysis - by Rajendra Bhatia
Linear Algebra in Action - by Harry Dym
Advanced Linear Algebra - by Steven Roman