Math 603 - Matrix Analysis

Class: MW 4:00PM - 5:15 online (8/27-12/8/2020), Instructor: Bedrich Sousedik

Topics in this course will include a review of basic matrix operations, determinants, rank, matrix inverse and solving linear equations. The course then will study partitioned matrices, eigenvalues and eigenvectors, spectral decomposition, singular-value decomposition, Jordan canonical form, orthogonal projections, idempotent matrices, quadratic forms, extrema of quadratic forms, non-negative definite and positive definite matrices, and matrix derivatives.

Prerequisite: MATH 221, 251 and 301 or permission of the instructor.

The detailed class syllabus (pdf) is here. However, look below to see the actual progress of the class.

Syllabus of the master's comprehensive exam can be found here.

eigenvectors and eigenvalues explained visually

8/31 Introduction.

9/2 Chapter 1: Linear Equations.

9/7 Labor day

9/9 Chapter 2: Rectangular systems and echelon form.

9/14 3.2-3.6 Matrix algebra.

9/16 3.7-3.8 Matrix inversion, inverses of sums. HW1 (due 9/30).

9/21 3.9-3.10 Elementary matrices, LU factorization.

9/23 4.1 Spaces and subspaces. 4.2 Four fundamental subspaces.

9/28 4.3 Linear independence. 4.4 Basis and dimension.

9/30 4.5 More about rank.

10/5 4.6 Classical least squares.

10/7 4.7 Linear transformations. 4.8 Change of basis and similarity. HW2 (due 10/19).

10/12 4.9 Invariant subspaces.

10/14 5.1-2 Vector and matrix norms. 5.3 Inner product spaces. 5.4 Orthogonal vectors.

10/19 5.5 Gram-Schmidt procedure. 5.6 Unitary and orthogonal matrices. 5.7 Orthogonal reduction.

10/21 (Study day.)

10/26 Exam #1 (Sections 3.7, 3.9, and 4.1-5.4).

10/28 5.9 Complementary subspaces. 5.10 Range-nullspace decomposition.

11/2 5.11 Orthogonal decomposition. 5.13 Orthogonal projection. (just notes: 6.1 Determinants.)

11/4 7.1 Elementary properties of eigensystems. HW3 (due 10/16).

11/9 7.2 Diagonalization by similarity transformations. HW4 (due 11/18).

11/11 7.5 Normal matrices.

11/16 7.6 Positive definite matrices.

11/18 (Study day.)

11/23 Exam #2 (Ch. 5).

11/25 (Thanksgiving, no class.)

11/30 (optional) 5.12 Singular value decomposition.

12/2 (optional) 7.7 Nilpotent matrices and Jordan structure.

12/7 (optional) 7.8 Jordan form.

Monday 12/14, 3:30-5:30pm Final.