| PDF Link | Lecture Topics |
|---|---|
| Lecture 1 | Column and Row Space Visualization of Matrix [Really awesome lecture] |
| Lecture 2 | Elimination, Back-Substitution, Elimination Matrices, Matrix Multiplication |
| Lecture 3 | Matrix Multiplication, Matrix Inversion, Gauss-Jordan |
| Lecture 4 | Inverse of AB, Product of Elimination Matrices, A=LU |
| Lecture 5 | PA=LU, Vector Spaces and Subspaces |
| Lecture 6 | Vector Spaces and Subspaces |
| Lecture 7 | Algorithm for Finding the Nullspace [Ax=0] |
| Lecture 8 | Complete Solution of Ax=b |
| Lecture 9 | Linear Independence, Spanning a Space, Basis, Dimension |
| Lecture 10 | The Four Fundamental Subspaces |
| Lecture 11 | Bases of Vector Spaces, Rank 1 Matrices |
| Lecture 12 | Graphs and Networks |
| Lecture 13 | Review Practice Problems |
| Lecture 14 | Orthogonal Vectors and Subspaces |
| Lecture 15 | Projection, Least Squares, Projection Matrix |
| Lecture 16 | Projection Matrices, Least Squared continued |
| Lecture 17 | Orthogonal Basis, Gram-Schmidt, Orthogonal Matrix |
| Lecture 18 | Determinants 1/2 |
| Lecture 19 | Determinants 2/2, Cofactor Expansion |
| Lecture 20 | Matrix Inversion and Determinants [Great Lecture, Lost Notes...] |
| Lecture 21 | Introduction to Eigenvalues and Eigenvectors |
| Lecture 22 | Matrix Diagonalization [S-1 * A * S = L], Powers of A, Fibonacci Example [*] |
| Lecture 23 | Application of Linear Algebra to Differential Equations |
| Lecture 24a | Markov Matrices and Fourier Series |
| Lecture 24b | Review and Practice Problems |
| Lecture 25 | Symmetric Matrices Facts |
| Lecture 26 | Complex Vectors and Matrices, Fourier Matrix, FFT [Matrix Factorization] |
| Lecture 27 | Positive Definite Matrices |
| Lecture 28 | Positive Definite Matrices, Similar Matrices |
| Lecture 29 | Singular Value Decomposition [SVD] |
| Lecture 30 | Linear Transformations |
| Lecture 31 | Change of Basis, Image Compression |
| Lecture 32 | Review and Practice Problems |
| Lecture 33 | Inverses, Course Review |
| Lecture 34 | Review |