8:01
Linear Systems and Solutions
Professor Heather Pierce
8:16
Linear Systems and Matrices
4:49
Reduced Row Echelon Form
5:15
More with REF and RREF
15:29
Solving Linear Systems
7:01
Systems with No Solutions
8:05
Systems with Infinte Solutions
8:44
Homogeneous Systems
7:27
Related Nonhomogeneous Systems
7:51
Matrix Addition
4:23
Scalar Multiplication
3:13
Matrix-Vector Multiplication
9:42
Matrix Multiplication
3:11
Transpose and Trace
6:16
Inverse of a Matrix
4:48
Elementary Matrices
10:27
Finding the Inverse
2:06
Inverses and Linear Systems
5:08
Properties of the Inverse
7:19
Invertible Matrix Theorem
4:19
Graphical Description of Vectors
4:14
Linear Combinations
3:41
Span of Vectors
8:31
Linear Independence
2:33
Parametric Vector Form
6:28
Describing a Line
2:52
Describing a Plane
5:02
Partitioned Matrices
7:53
LU Factorization
7:26
Linear Transformations
7:43
Matrix Transformations
4:03
Properties of Transformations
13:20
Determinants
4:55
Properties of the Determinant
4:21
Determinants and Row Operations
5:55
Cofactors and the Inverse
6:44
Determinants and Area
9:43
Cramer's Rule
11:18
Vector Spaces
6:08
Properties of Vector Spaces
10:20
Subspaces
10:28
Basis of R^n
2:37
Basis for Polynomials
4:15
Basis for Functions
3:26
The Column Space
3:53
The Null Space
1:24
The Row Space
1:57
The Rank Theorem
6:47
Coordinate Vectors
8:22
Change of Basis
9:55
Eigenvectors
9:03
Eigenvalues
Complex Eigenvalues and Eigenvectors
7:23
Diagonalization
4:02
The Dot Product
5:40
Length of Vectors
Orthogonal Vectors
8:55
Gram Schmidt Process
11:00
Least Squares Solutions
Dynamical Systems
8:46
Markov Chains
6:50
Powers of Transition Matrices
7:12
Orthogonal Matrices
9:54
Orthogonal Diagonalization
7:58
Singular Value Decomposition
