Dr. Bob's Online Linear Algebra

Online Linear Algebra
with online videos Dr. Bob's Online University
(Not an actual university)
Robert 'Dr. Bob' Gardner

This website includes links to class notes and supplements (in PDF) used in the teaching of East Tennessee State University's sophomore level Linear Algebra (MATH 2010). Links are also available for video presentations of the notes. The videos have been used as of the teaching of online Linear Algebra, starting in spring 2020. The material is based closely on John B. Fraleigh and Raymond A. Beauregard's Linear Algebra, 3rd edition, Addison-Wesley Publishing (1995):

Fraleigh and Beauregard's Linear Algebra book, 3rd edition

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 can be streamed from YouTube and should remain permanently available. (The videos previously on ETSU's Panopto host site have been, or may soon be, deleted.)

Chapter 1. Vectors, Matrices, and Linear Systems.

SECTION	NOTES	SUPPLEMENTS	VIDEOS ON YOUTUBE
1.1. Vectors in Euclidean Spaces	1.1 Notes	1.1 Supplement 1.1 Supplement Print File	1.1 Video, Part 1 (30:50) 1.1 Video, Part 2 (49:02)
1.2. The Norm and Dot Product	1.2 Notes	1.2 Supplement 1.2 Supplement Print File	1.2 Video (1:26:00)
1.3. Matrices and Their Algebra	1.3 Notes	1.3 Supplement 1.3 Supplement Print File	1.3 Video (1:00:09)
1.4. Solving Systems of Linear Equations	1.4 Notes	1.4 Supplement 1.4 Supplement Print File	1.4 Video, Part 1 (1:05:21) 1.4 Video, Part 2 (1:05:21)
1.5. Inverses of Square Matrices	1.5 Notes	1.5 Supplement 1.5 Supplement Print File	1.5 Video, Part 1 (48:34) 1.5 Video, Part 2 (27:44)
1.6. Homogeneous Systems, Subspaces, and Bases	1.6 Notes	1.6 Supplement 1.6 Supplement Print File	1.6 Video, Part 1 (44:17) 1.6 Video, Part 2 (46:28)
1.7. Application to Population Distributions	1.7 Notes	1.7 Supplement 1.7 Supplement Print File	-

Chapter 2. Dimension, Rank, and Linear Transformations.

SECTION	NOTES	SUPPLEMENTS	VIDEOS ON YOUTUBE
2.1. Independence and Dimension	2.1 Notes	2.1 Supplement 2.1 Supplement Print File	-
2.2. The Rank of a Matrix	2.2 Notes	2.2 Supplement 2.2 Supplement Print File	-
2.3. Linear Transformations of Euclidean Spaces	2.3 Notes	2.3 Supplement 2.3 Supplement Print File	-
2.4. Linear Transformations of the Plane	2.4 Notes	2.4 Supplement 2.4 Supplement Print File	-
2.5. Lines, Planes, and Other Flats	2.5 Notes	2.5 Supplement 2.5 Supplement Print File	-

Chapter 3. Vector Spaces.

SECTION	NOTES	SUPPLEMENTS	VIDEOS ON YOUTUBE
3.1. Vector Spaces	3.1 Notes	3.1 Supplement 3.1 Supplement Print File	-
3.2. Basic Concepts of Vector Spaces	3.2 Notes	3.2 Supplement 3.2 Supplement Print File	-
3.3. Coordinatization of Vectors	3.3 Notes	3.3 Supplement 3.3 Supplement Print File	-
3.4. Linear Transformations	3.4 Notes	3.4 Supplement 3.4 Supplement Print File	-
3.5. Inner-Product Spaces	3.5 Notes	3.5 Supplement 3.5 Supplement Print File	-

Chapter 4. Determinants.

SECTION	NOTES	SUPPLEMENTS	VIDEOS ON YOUTUBE
4.1. Areas, Volumes, and Cross Products	4.1 Notes	4.1 Supplement 4.1 Supplement Print File	4.1 Video, Part 1 (31:39) 4.1 Video, Part 2 (38:37)
4.2. The Determinant of a Square Matrix	4.2 Notes	4.2 Supplement 4.2 Supplement Print File	4.2 Video, Part 1 (38:45) 4.2 Video, Part 2 (27:28)
4.3. Computation of Determinants and Cramer's Rule	4.3 Notes	4.3 Supplement 4.3 Supplement Print File	4.3 Video, Part 1 (18:33) 4.3 Video, Part 2 (31:24)
4.4. Linear Transformations and Determinants	4.4 Notes	4.4 Supplement 4.4 Supplement Print File	-

Chapter 5. Eigenvalues and Eigenvectors.

SECTION	NOTES	SUPPLEMENTS	VIDEOS ON YOUTUBE
5.1. Eigenvalues and Eigenvectors	5.1 Notes	5.1 Supplement 5.1 Supplement Print File	5.1 Video, Part 1 (25:48) 5.1 Video, Part 2 (28:06) 5.1 Video, Part 3 (21:14)
5.2. Diagonalization	5.2 Notes	5.2 Supplement 5.2 Supplement Print File	5.2 Video, Part 1 (52:36) 5.2 Video, Part 2 (47:09)
5.3. Two Applications	5.3 Notes	5.3 Supplement 5.3 Supplement Print File	-

Chapter 6. Eigenvalues and Eigenvectors.

SECTION	NOTES	SUPPLEMENTS	VIDEOS ON YOUTUBE
6.1. Projections	6.1 Notes	6.1 Supplement 6.1 Supplement Print File	6.1 Video (55:08)
6.2. The Gram-Schmidt Process	6.2 Notes	6.2 Supplement 6.2 Supplement Print File	6.2 Video, Part 1 (21:57) 6.2 Video, Part 2 (40:40) 6.2 Video, Part 3 (16:47)
6.3. Orthogonal Matrices	6.3 Notes	6.3 Supplement 6.3 Supplement Print File	-
6.4. The Projection Matrix	6.4 Notes	6.4 Supplement 6.4 Supplement Print File	-
6.5. The Method of Least Squares	6.5 Notes	6.5 Supplement 6.5 Supplement Print File	-

Additional notes and supplements based on Fraleigh and Beauregard's Linear Algebra are available on the Linear Algebra Class Notes webpage.

Return to Dr. Bob's webpage

Last updated: March 11, 2024.