Matrix Algebra for Engineers 

Promotional Video

Introduction

Definition of a Matrix

Lecture 1

Addition and Multiplication of Matrices

Lecture 2

Special Matrices

Lecture 3

Transpose Matrix

Lecture 4

Inner and Outer Products

Lecture 5

Inverse Matrix

Lecture 6

Orthogonal Matrices

Lecture 7

Rotation Matrices

Lecture 8

Permutation Matrices

Lecture 9

Welcome and Course Information

How to Write Math in the Discussions Using MathJax

Construct Some Matrices

Matrix Addition and Multiplication

AB=AC Does Not Imply B=C

Matrix Multiplication Does Not Commute

Associative Law for Matrix Multiplication

AB=0 When A and B Are Not zero

Product of Diagonal Matrices

Product of Triangular Matrices

Transpose of a Matrix Product

Any Square Matrix Can Be Written as the Sum of a Symmetric and Skew-Symmetric Matrix

Construction of a Square Symmetric Matrix

Example of a Symmetric Matrix

Sum of the Squares of the Elements of a Matrix

Inverses of Two-by-Two Matrices

Inverse of a Matrix Product

Inverse of the Transpose Matrix

Uniqueness of the Inverse

Product of Orthogonal Matrices

The Identity Matrix is Orthogonal

Inverse of the Rotation Matrix

Three-dimensional Rotation

Three-by-Three Permutation Matrices

Inverses of Three-by-Three Permutation Matrices

Diagnostic Quiz

Matrix Definitions

Transposes and Inverses

Orthogonal Matrices

Week One Assessment

Introduction

Gaussian Elimination

Lecture 10

Reduced Row Echelon Form

Lecture 11

Computing Inverses

Lecture 12

Elementary Matrices

Lecture 13

LU Decomposition

Lecture 14

Solving (LU)x = b

Lecture 15

Gaussian Elimination

Reduced Row Echelon Form

Computing Inverses

Elementary Matrices

LU Decomposition

Solving (LU)x = b

Gaussian Elimination

LU Decomposition

Week Two Assessment

Introduction

Vector Spaces

Lecture 16

Linear Independence

Lecture 17

Span, Basis and Dimension

Lecture 18

Gram-Schmidt Process

Lecture 19

Gram-Schmidt Process Example

Lecture 20

Null Space

Lecture 21

Application of the Null Space

Lecture 22

Column Space

Lecture 23

Row Space, Left Null Space and Rank

Lecture 24

Orthogonal Projections

Lecture 25

The Least-Squares Problem

Lecture 26

Solution of the Least-Squares Problem

Lecture 27

Zero Vector

Examples of Vector Spaces

Linear Independence

Orthonormal basis

Gram-Schmidt Process

Gram-Schmidt on Three-by-One Matrices

Gram-Schmidt on Four-by-One Matrices

Null Space

Underdetermined System of Linear Equations

Column Space

Fundamental Matrix Subspaces

Orthogonal Projections

Setting Up the Least-Squares Problem

Line of Best Fit

Vector Space Definitions

Gram-Schmidt Process

Fundamental Subspaces

Orthogonal Projections

Week Three Assessment

Introduction

Two-by-Two and Three-by-Three Determinants

Lecture 28

Laplace Expansion

Lecture 29

Leibniz Formula

Lecture 30

Properties of a Determinant

Lecture 31

The Eigenvalue Problem

Lecture 32

Finding Eigenvalues and Eigenvectors (1)

Lecture 33

Finding Eigenvalues and Eigenvectors (2)

Lecture 34

Matrix Diagonalization

Lecture 35

Matrix Diagonalization Example

Lecture 36

Powers of a Matrix

Lecture 37

Powers of a Matrix Example

Lecture 38

Concluding Remarks

Determinant of the Identity Matrix

Row Interchange

Determinant of a Matrix Product

Compute Determinant Using the Laplace Expansion

Compute Determinant Using the Leibniz Formula

Determinant of a Matrix With Two Equal Rows

Determinant is a Linear Function of Any Row

Determinant Can Be Computed Using Row Reduction

Compute Determinant Using Gaussian Elimination

Characteristic Equation for a Three-by-Three Matrix

Eigenvalues and Eigenvectors of a Two-by-Two Matrix

Eigenvalues and Eigenvectors of a Three-by-Three Matrix

Complex Eigenvalues

Linearly Independent Eigenvectors

Invertibility of the Eigenvector Matrix

Diagonalize a Three-by-Three Matrix

Matrix Exponential

Powers of a Matrix

Please Rate this Course

Acknowledgments

Determinants

The Eigenvalue Problem

Matrix Diagonalization

Week Four Assessment