Robert Gardner's Online Theory of Matrices

Online Theory of Matrices with Zoom videos Dr. Bob's Online University
(Not an actual university)

This website includes links to class notes and supplements (in PDF) used in the teaching of East Tennessee State University's graduate-only level Theory of Matrices (MATH 5090). Links are also available for video presentations of the notes. The videos have been used as of the teaching of online Theory of Matrices, starting in summer 2020. The material is based closely on James E. Gentle's Matrix Algebra: Theory, Computations, and Applications in Statistics, Springer (2007):

Robert "Dr. Bob" Gardner can be reached by e-mail at: gardnerr@etsu.edu. His office is in Gilbreath Hall, Room 308F on the ETSU campus.

The following notes and supplements are all in PDF. The videos are stream from Zoom and include a synchronized transcript. However, ETSU does not have control of the Zoom site and these videos may be taken down as some point. For versions of these videos in mp4 housed on ETSU's Panopto Host, see the "Online Theory of Matrices with Videos on ETSU's Panopto Host" webpage.There are a few small errors in the videos when the online notes and supplements are referenced, but all known errors are corrected in versions of the notes and supplements updated since the recording of the videos.

Chapter 1. Basic Vectors/Matrix Structure and Notation.

SECTION	NOTES	SUPPLEMENTS	VIDEOS
Chapter 1. Basic Vector/Matrix Structure and Notation	Chapter 1 Notes	-	Chapter 1 Video (9:13)

Chapter 2. Vectors and Vector Spaces.

SECTION	NOTES	SUPPLEMENTS	VIDEOS
2.1. Operations on Vectors	2.1 Notes	2.1 Supplement 2.1 Supplement Print File	2.1 Video, Part 1 (53:53) 2.1 Video, Part 2 (58:08) 2.1 Video, Part 3 (1:04:24)
2.2. Cartesian Coordinates and Geometrical Properties of Vectors	2.2 Notes	2.2 Supplement 2.2 Supplement Print File	2.2 Video, Part 1 (36:50) 2.2 Video, Part 2 (54:41)
2.3. Centered Vectors and Variances and Covariances of Vectors	2.3 Notes	2.3 Supplement 2.3 Supplement Print File	2.3 Video (46:54)

Chapter 3. Basic Properties of Matrices.

SECTION	NOTES	SUPPLEMENTS	VIDEOS
3.1. Basic Definitions and Notation	3.1 Notes	3.1 Supplement 3.1 Supplement Print File	3.1 Video, Part 1 (59:16) 3.1 Video, Part 2 (49:52) 3.1 Video, Part 3 (45:30) 3.1 Video, Part 4 (1:00:04) 3.1 Video, Part 5 (58:15)
3.2. Multiplication of Matrices and Multiplication of Vectors and Matrices	3.2 Notes	3.2 Supplement 3.2 Supplement Print File	3.2 Video, Part 1 (46:23) 3.2 Video, Part 2 (28:15) 3.2 Video, Part 3 (1:17:27)
3.3. Matrix Rank and the Inverse of a Full Rank Matrix	3.3 Notes	3.3 Supplement 3.3 Supplement Print File	3.3 Video, Part 1 (59:41) 3.3 Video, Part 2 (25:16) 3.3 Video, Part 3 (59:41) 3.3 Video, Part 4 (47:41) 3.3 Video, Part 5 (21:28)
3.4. More on Partitioned Square Matrices: The Schur Complement	3.4 Notes	3.4 Supplement 3.4 Supplement Print File	3.4 Video (35:45)
3.5. Linear Systems of Equations	3.5 Notes	3.5 Supplement 3.5 Supplement Print File	3.5 Video, Part 1 (51:32) 3.5 Video, Part 2 (27:32)
3.6. Generalized Inverses	3.6 Notes	3.6 Supplement 3.6 Supplement Print File	3.6 Video, Part 1 (23:03) 3.6 Video, Part 2 (19:10)
3.7. Orthogonality	3.7 Notes	3.7 Supplement 3.7 Supplement Print File	3.7 Video (40:19)
3.8. Eigenanalysis; Canonical Factorizations	3.8 Notes	3.8 Supplement 3.8 Supplement Print File	3.8 Video, Part 1 (29:08) 3.8 Video, Part 2 (1:08:34) 3.8 Video, Part 3 (41:40) 3.8 Video, Part 4 (1:28:08) 3.8 Video, Part 5 (1:24:13)
3.9. Matrix Norms	3.9 Notes	3.9 Supplement 3.9 Supplement Print File	3.9 Video, Part 1 (49:39) 3.9 Video, Part 2 (1:12:16)
3.10. Approximation of Matrices	3.10 Notes	-	-

Chapter 4. Vector/Matrix Derivatives and Integrals.

SECTION	NOTES	SUPPLEMENTS	VIDEOS
4.1. Basics of Differentiation	4.1 Notes	-	-
4.2. Types of Differentiation	4.2 Notes	4.2 Supplement 4.2 Supplement Print File	-
4.3. Optimization of Functions (Partial)	4.3 Notes	-	-
4.4. Multiparameter Likelihood Functions	4.4 Notes	-	-
4.5. Integration and Expectation	4.5 Notes	4.5 Supplement 4.5 Supplement Print File	-

Chapter 5. Matrix Transformations and Factorizations.

SECTION	NOTES	SUPPLEMENTS	VIDEOS
5.1. Transformations by Orthogonal Matrices	5.1 Notes	-	5.1 Video (6:07)
5.2. Geometric Transformations	5.2 Notes	-	5.2 Video (44:23)
5.3. Householder Transformations (Reflections)	5.3 Notes	5.3 Supplement 5.3 Supplement Print File	5.3 Video (31:32)
5.4. Givens Transformations (Rotations)	5.4 Notes	-	5.4 Video (27:01)
5.5. Factorizations of Matrices	5.5 Notes	-	5.5 Video (4:12)
5.6. LU and LDU Factorizations	5.6 Notes	5.6 Supplement 5.6 Supplement Print File	5.6 Video (39:06)
5.7. QR Factorization	5.7 Notes	5.7 Supplement 5.7 Supplement Print File	5.7 Video (22:57)
5.8. Singular Value Factorization	5.8 Notes	-	5.8 Video (3:47)
5.9. Factorizations of Nonnegative Definite Matrices	5.9 Notes	5.9 Supplement 5.9 Supplement Print File	5.9 Video (41:56)
5.10. Incomplete Factorizations	5.10 Notes	-	5.10 Video (2:46)

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Last updated: December 10, 2020.