Linear Algebra (video)
Linear Algebra (video)
Video Lectures | MPEG4 Video 480x360 25.00fps | AAC 44100Hz stereo 1411Kbps | 34 lectures, (40 :50) minutes/lecture | 3.55 GB
This is a basic subject on matrix theory and linear algebra. Emphasis is given to topics that will be useful in other disciplines, including systems of equations, vector spaces, determinants, eigenvalues, similarity, and positive definite matrices.
Course Features
1 The Geometry of Linear Equations
2 Elimination with Matrices
3 Multiplication and Inverse Matrices
4 Factorization into A = LU
5 Transposes, Permutations, Spaces R^n
6 Column Space and Nullspace
7 Solving Ax = 0: Pivot Variables, Special Solutions
8 Solving Ax = b: Row Reduced Form R
9 Independence, Basis, and Dimension
10 The Four Fundamental Subspaces
11 Matrix Spaces; Rank 1; Small World Graphs
12 Graphs, Networks, Incidence Matrices
13 Quiz 1 Review
14 Orthogonal Vectors and Subspaces
15 Projections onto Subspaces
16 Projection Matrices and Least Squares
17 Orthogonal Matrices and Gram-Schmidt
18 Properties of Determinants
19 Determinant Formulas and Cofactors
20 Cramer's Rule, Inverse Matrix, and Volume
21 Eigenvalues and Eigenvectors
22 Diagonalization and Powers of A
23 Differential Equations and exp(At)
24 Markov Matrices; Fourier Series
24b Quiz 2 Review
25 Symmetric Matrices and Positive Definiteness
26 Complex Matrices; Fast Fourier Transform
27 Positive Definite Matrices and Minima
28 Similar Matrices and Jordan Form
29 Singular Value Decomposition
30 Linear Transformations and Their Matrices
31 Change of Basis; Image Compression
32 Quiz 3 Review
33 Left and Right Inverses; Pseudoinverse
34 Final Course Review