24:31
Change of Variables in Integration in R^n
20:20
Determinant of an Operator and of a Matrix
15:53
Trace of an Operator and of a Matrix
10:53
Change of Basis
08:06
Isometries on Real Inner Product Spaces
09:09
Normal Operators on Real Inner Product Spaces
19:40
Complexification
10:29
Jordan Form
15:35
The Minimal Polynomial
07:00
The Characteristic Polynomial
09:01
Square Roots of Operators
04:32
Block Diagonal Matrices
12:49
Decomposition Via Generalized Eigenvectors
06:11
Nilpotent Operators
12:57
Generalized Eigenvectors
11:12
Null Spaces of Powers of an Operator
16:47
Singular Value Decomposition
12:29
Polar Decomposition
17:16
Isometries
14:45
Positive Operators
11:18
The Spectral Theorem
09:33
Normal Operators
09:01
Self-Adjoint Operators
13:16
Adjoints
08:51
Minimization Problems
09:00
Orthogonal Complements
14:12
Orthonormal Bases
12:46
Norms
11:18
Inner Products
11:31
Eigenspaces and Diagonal Matrices
09:00
Upper Triangular Matrices
14:33
Existence of Eigenvalues
16:55
Invariant Subspaces
12:08
Polynomials
15:42
Annihilators and the Matrix of a Dual Map
11:33
Dual Bases and Dual Maps
09:07
Quotients of Vector Spaces
07:26
Products of Vector Spaces
13:55
Invertibility and Isomorphic Vector Spaces
13:20
Matrix Multiplication
12:20
The Matrix of a Linear Map
15:25
Null Spaces And Ranges
14:02
Vector Space of Linear Maps
10:08
Dimension
09:35
Bases
13:41
Span and Linear Independence
10:12
Subspaces
08:51
Definition of Vector Space
10:09
R^n and C^n
04:21
Introduction
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