Using Matrices to Solve Systems of Linear Equations
4
Reduced Row Echelon Form
5
Gaussian Elimination
6
Existence and Uniqueness of Solutions
7
Linear Equations Setup
8
Matrix Addition and Scalar Multiplication
9
Matrix Multiplication
10
Properties of Matrix Multiplication
11
Interpretations of Matrix Multiplication
12
Introduction to Vectors (Math 210)
13
Solving Vector Equations
14
Solving Matrix Equations
15
Matrix Inverses
16
Matrix Inverses for 2x2 Matrices
17
Equivalent Conditions for a Matrix to be Invertible
18
Properties of Matrix Inverses
19
Transpose
20
Symmetric and Skew-symmetric Matrices
21
Trace
22
The Determinant of a Matrix
23
Determinant and Elementary Row Operations
24
Determinant Properties.
25
Invertible Matrices and Their Determinants
26
Eigenvalues and Eigenvectors
27
Properties of Eigenvalues
28
Diagonalizing Matrices
29
Dot Product (Linear Algebra)
30
Unit Vectors
31
Orthogonal Vectors
32
Orthogonal Matrices
33
Symmetric Matrices and Eigenvectors and Eigenvalues
34
Symmetric Matrices and Eigenvalues and Eigenvectors - Proofs
35
Diagonalizing Symmetric Matrices
36
Linearly Independent Vectors
37
Gram-Schmidt Orthogonalization
38
Singular Value Decomposition - Introduction
39
Singular Value Decomposition - How To Find It
40
Singular Value Decomposition - Why It Works
Description:
Dive into a comprehensive 7-hour course on Linear Algebra, covering essential topics from linear equations to advanced matrix operations. Master solving systems of linear equations, Gaussian elimination, and matrix multiplication. Explore vector operations, determinants, eigenvalues, and eigenvectors. Learn about orthogonality, Gram-Schmidt orthogonalization, and the Singular Value Decomposition. Gain a solid foundation in linear algebra concepts and techniques applicable to various fields of mathematics and science.