Category:

# Linear Algebra

Duration: 41:22:00
Lectures: 52
Level: Beginner Systems of linear equations, Matrices, Elementary row operations, Row-reduced echelon matrices .Vector spaces,
Subspaces, Bases and dimension, Ordered bases and coordinates.

Linear transformations, Rank-nullity theorem, Algebra of linear transformations, Isomorphism, Matrix representation, Linear
functionals, Annihilator, Double dual, Transpose of a linear transformation. Characteristic values and characteristic vectors of linear

transformations, Diagonalizability, Minimal polynomial of a linear transformation, Cayley-Hamilton theorem, Invariant subspaces,
Direct-sum decompositions, Invariant direct sums, The primary decomposition theorem, Cyclic subspaces and annihilators,
Cyclic decomposition, Rational, Jordan forms. Inner product spaces, Orthonormal bases, Gram-Schmidt process.

1
Linear Algebra -Lec :1-Introduction to the Course Contents.
26:46
2
Linear Algebra -Lec :2-Linear Equations
35:10
3
Linear Algebra -Lec :3a-Equivalent Systems of Linear Equations I: Inverses of Elementary Row-operations, Row-equivalent matrices
40;47
4
Linear Algebra -Lec :3b-Equivalent Systems of Linear Equations II: Homogeneous Equations, Examples
43:58
5
Linear Algebra -Lec :4-Row-reduced Echelon Matrices
48:22
6
Linear Algebra -Lec :5-Row-reduced Echelon Matrices and Non-homogeneous Equations
47:18
7
Linear Algebra -Lec :6-Elementary Matrices, Homogeneous Equations and Non-homogeneous Equations
49:13
8
Linear Algebra -Lec :7-Invertible matrices, Homogeneous Equations Non-homogeneous Equations
50:58
9
Linear Algebra -Lec :8-Vector spaces
34:43
10
Linear Algebra -Lec :9-Elementary Properties in Vector Spaces. Subspaces
48:16
11
Linear Algebra -Lec :10-Subspaces (continued), Spanning Sets, Linear Independence, Dependence
43:25
12
Linear Algebra -Lec :11- Basis for a vector space
48:48
13
Linear Algebra -Lec :12-Dimension of a vector space
48:31
14
Linear Algebra -Lec :13- Dimensions of Sums of Subspaces
52:11
15
Linear Algebra -Lec :14-Linear Transformations
50;10
16
Linear Algebra -Lec :15-The Null Space and the Range Space of a Linear Transformation
51:04
17
Linear Algebra -Lec :16-The Rank-Nullity-Dimension Theorem. Isomorphisms Between Vector Spaces
41:44
18
Linear Algebra -Lec :17-Isomorphic Vector Spaces, Equality of the Row-rank and the Column-rank I
47:34
19
Linear Algebra -Lec :18-Equality of the Row-rank and the Column-rank II
36:08
20
Linear Algebra -Lec :19-The Matrix of a Linear Transformation
40;27
21
Linear Algebra -Lec :20-Matrix for the Composition and the Inverse. Similarity Transformation
47:04
22
Linear Algebra -Lec :21-Linear Functionals. The Dual Space. Dual Basis I
49:19
23
Linear Algebra -Lec :22-Dual Basis II. Subspace Annihilators I
38:53
24
Linear Algebra -Lec :23-Subspace Annihilators II
50:07
25
Linear Algebra -Lec :24-The Double Dual. The Double Annihilator
47:34
26
Linear Algebra -Lec :25-The Transpose of a Linear Transformation. Matrices of a Linear Transformation and its Transpose
45:21
27
Linear Algebra -Lec :26-Eigenvalues and Eigenvectors of Linear Operators
40:11
28
Linear Algebra -Lec :27-Diagonalization of Linear Operahttp. A Characterization
47:01
29
Linear Algebra -Lec :28-The Minimal Polynomial
42:37
30
Linear Algebra -Lec :29-The Cayley-Hamilton Theorem
47:21
31
Linear Algebra -Lec :30-Invariant Subspaces
39:18
32
Linear Algebra -Lec :31-Triangulability, Diagonalization in Terms of the Minimal Polynomial
51:29
33
Linear Algebra -Lec :32-Independent Subspaces and Projection Operators
48:41
34
Linear Algebra -Lec :33-Direct Sum Decompositions and Projection Operators I
48:48
35
Linear Algebra -Lec :34-Direct Sum Decomposition and Projection Operators II
46:39
36
Linear Algebra -Lec :35-The Primary Decomposition Theorem and Jordan Decomposition
38:50
37
Linear Algebra -Lec :36-Cyclic Subspaces and Annihilators
50:46
38
Linear Algebra -Lec :37-The Cyclic Decomposition Theorem I
49:55
39
Linear Algebra -Lec :38-The Cyclic Decomposition Theorem II. The Rational Form
46:11
40
Linear Algebra -Lec :39- Inner Product Spaces
44:43
41
Linear Algebra -Lec :40- Norms on Vector spaces. The Gram-Schmidt Procedure I
53:20
42
Linear Algebra -Lec :41-The Gram-Schmidt Procedure II. The QR Decomposition.
43:09
43
Linear Algebra -Lec :42- Bessel’s Inequality, Parseval’s Indentity, Best Approximation
41:53
44
Linear Algebra -Lec :43- Best Approximation: Least Squares Solutions
50:36
45
Linear Algebra -Lec :44- Orthogonal Complementary Subspaces, Orthogonal Projections
50:00
46
Linear Algebra -Lec :45-Projection Theorem. Linear Functionals
47:27
47
Linear Algebra -Lec :46-The Adjoint Operator
48:20
48
Linear Algebra -Lec :47- Properties of the Adjoint Operation. Inner Product Space Isomorphism
52:36
49
Linear Algebra -Lec :48- Unitary Operators
48:17
50
Linear Algebra -Lec :49-Unitary operators II. Self-Adjoint Operators I.
42:11
51
Linear Algebra -Lec :50-Self-Adjoint Operators II – Spectral Theorem
41:07
52
Linear Algebra -Lec :51- Normal Operators – Spectral Theorem
46:09