 INTRODUCTION TO MATRIX ALGEBRA Transforming Matrix Algebra for the STEM Undergraduate HOME | TOPICS | VIDEOS | TEXTBOOK | PPT | QUIZZES | PROBLEM SET | CONTACT | MATH FOR COLLEGE | NUMERICAL METHODS
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 CHAPTER 01.   INTRODUCTION [MORE] What is a matrix? [YOUTUBE 2:22] [TRANSCRIPT]   What is a row vector?  [YOUTUBE 1:24] [TRANSCRIPT] What is a column vector? [YOUTUBE 1:58] [TRANSCRIPT]   What is a submatrix? [YOUTUBE 2:44] [TRANSCRIPT]   What is a square matrix? [YOUTUBE 1:44] [TRANSCRIPT]   What is an upper triangular matrix? [YOUTUBE 3:02]  [TRANSCRIPT] What is a lower triangular matrix? [YOUTUBE 3:14]  [TRANSCRIPT] What is an identity matrix? [YOUTUBE 2:02] [TRANSCRIPT] Diagonally dominant matrix [YOUTUBE 7:22]  [TRANSCRIPT]   Equal matrices [YOUTUBE 2:54]  [TRANSCRIPT]

CHAPTER 05.  SYSTEM OF EQUATIONS [MORE]

A real life problem of setting up simultaneous linear equations [YOUTUBE 5:23] [TRANSCRIPT]

Writing simultaneous linear equations in matrix form  [YOUTUBE 5:25] [TRANSCRIPT]

Consistent and inconsistent system of equations Theory [YOUTUBE 2:56] [TRANSCRIPT]

Consistent and inconsistent system of equations Example [YOUTUBE 5:31] [TRANSCRIPT]

Rank of a matrix Definition [YOUTUBE 1:21] [TRANSCRIPT]

Rank of a matrix Example 1 [YOUTUBE 1:31]  [TRANSCRIPT]

Rank of a matrix Example 2  [YOUTUBE 2:50]  [TRANSCRIPT]

Distinguishing between consistent and inconsistent system of equations based on rank of matrices [YOUTUBE 3:06] [TRANSCRIPT]

Distinguishing between consistent and inconsistent system of equations based on rank of matrices Example 1 [YOUTUBE 4:15]  [TRANSCRIPT]
Distinguishing between consistent and inconsistent system of equations based on rank of matrices Example 2  [YOUTUBE 8:42]  [TRANSCRIPT]

Distinguishing between consistent and inconsistent system of equations based on rank of matrices Example 3 [YOUTUBE 6:07]  [TRANSCRIPT]

If a solution  exists, how do we know if it is unique?  [YOUTUBE 3:25]  [TRANSCRIPT]

Does a set of equations have a unique solution? Example 1  [YOUTUBE 2:18] [TRANSCRIPT]

Does a set of equations have a unique solution? Example 2 [YOUTUBE 2:23]  [TRANSCRIPT]
If we have more equations than unknowns, does it mean we have inconsistent system of equations?  [YOUTUBE 8:11]  [TRANSCRIPT]

Can a system of equations have more then one but not infinite number of solutions?  [YOUTUBE 4:57] [TRANSCRIPT]

Can we divide two matrices?  [YOUTUBE 5:39]  [TRANSCRIPT]

Inverse of matrices Example  [YOUTUBE 3:40]  [TRANSCRIPT]

Using concept of inverse to solve a set of equations  [YOUTUBE 2:27]  [TRANSCRIPT]

Finding the inverse of a matrix Theory [YOUTUBE 4:32] [TRANSCRIPT]

Finding the inverse of a matrix Example  [YOUTUBE 7:03]  [TRANSCRIPT]
Finding the inverse of a matrix by adjoints Theory  [YOUTUBE 2:15]  [TRANSCRIPT]

Finding the inverse of a matrix by adjoints Example  [YOUTUBE 7:19] [TRANSCRIPT]

If the inverse of [A] exists, is it unique?  [YOUTUBE 2:30]  [TRANSCRIPT]

 CHAPTER 07.   LU DECOMPOSITION [MORE] LU Decomposition: Basis [YOUTUBE 9:02] [TRANSCRIPT] LU Decomposition Method: Example  [YOUTUBE 10:29] [TRANSCRIPT] Why LU Decomposition:  Part 1 [YOUTUBE 4:58][TRANSCRIPT] Why LU Decomposition:  Part 2 [YOUTUBE 8:05][TRANSCRIPT] Decomposing a Square Matrix:  Part 1 of 2 [YOUTUBE 6:56[TRANSCRIPT] Decomposing a Square Matrix:  Part 2 of 2 [YOUTUBE 4:37] [TRANSCRIPT] Finding Inverse of a Matrix Using LU Decomposition: Background [YOUTUBE 6:03] [TRANSCRIPT] Finding Inverse of a Matrix Using LU Decomposition: Example [YOUTUBE 10:20] [TRANSCRIPT]
 CHAPTER 08.   GAUSS-SEIDEL METHOD [MORE} Gauss-Seidel Method of Solving Simul Linear Eqns: Theory: Part 1 of 2 [YOUTUBE 8:01] [TRANSCRIPT] Gauss-Seidel Method of Solving Simul Linear Eqns: Theory: Part 2 of 2 [YOUTUBE 5:38] [TRANSCRIPT] Gauss-Seidel Method of Solving Simul Linear Eqns: Example: Part 1 of 2 [YOUTUBE 9:17] [TRANSCRIPT] Gauss-Seidel Method of Solving Simul Linear Eqns: Example: Part 2 of 2 [YOUTUBE 7:40] [TRANSCRIPT] Gauss-Seidel Method of Solving Simul Linear Eqns:                                                                        Pitfalls and Advantages: Part 1 of 2 [YOUTUBE 7:50] [TRANSCRIPT] Gauss-Seidel Method of Solving Simul Linear Eqns:                                                                        Pitfalls and Advantages: Part 2 of 2  [YOUTUBE 8:14] [TRANSCRIPT]

CHAPTER 10.  EIGENVALUES AND EIGENVECTORS [MORE]

What is the origin of the word eigenvalue [YOUTUBE 1:02] [TRANSCRIPT]

A physical example of application of eigenvalues and eigenvectors  [YOUTUBE 16:23] [TRANSCRIPT]

Definition of eigenvalues and eigenvectors  [YOUTUBE 3:11] [TRANSCRIPT]

How do I find eigenvalues of a square matrix  [YOUTUBE 4:33][TRANSCRIPT]

How do I find eigenvalues of a square matrix? Example [YOUTUBE 3:46][TRANSCRIPT]

How do I find eigenvectors of a square matrix? Example [YOUTUBE 6:33][TRANSCRIPT]

How do I find eigenvectors of a square matrix? Example 2 [YOUTUBE 13:10] [TRANSCRIPT]

Theorems of eigenvalues and eigenvectors Part 1 of 6 [YOUTUBE 2:19] [TRANSCRIPT]

Theorems of eigenvalues and eigenvectors Part 2 of 6  [YOUTUBE 2:06][TRANSCRIPT]

Theorems of eigenvalues and eigenvectors Part 3 of 6 [YOUTUBE 2:43] [TRANSCRIPT]
Theorems of eigenvalues and eigenvectors Part 4 of 6  [YOUTUBE 0:53] [TRANSCRIPT]

Theorems of eigenvalues and eigenvectors Part 5 of 6 [YOUTUBE 1:37] [TRANSCRIPT]

Theorems of eigenvalues and eigenvectors Part 6 of 6  [YOUTUBE 3:15] [TRANSCRIPT]

How does one find eigenvalues and eigenvectors numerically  [YOUTUBE 4:57] [TRANSCRIPT]

How does one find eigenvalues and eigenvectors numerically Example  [YOUTUBE 8:09][TRANSCRIPT]

 Copyrights: University of South Florida, 4202 E Fowler Ave, Tampa, FL 33620-5350. All Rights Reserved. Questions, suggestions or comments, contact kaw@usf.edu  This material is based upon work supported by the National Science Foundation under Grant# 0126793, 0341468, 0717624,  0836981, , 0836805, 1322586.  Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.  Based on a work at http://mathforcollege.com/ma.  Introduction to Matrix Algebra is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License.