Video Lectures

Lecture 1: The geometry of linear equations

Lecture 2: Elimination with matrices

Lecture 3: Multiplication and inverse matrices

Lecture 4: Factorization into A = LU

Lecture 5: Transposes, permutations, spaces R^n

Lecture 6: Column space and nullspace

Lecture 7: Solving Ax = 0: pivot variables, special solutions

Lecture 8: Solving Ax = b: row reduced form R

Lecture 9: Independence, basis, and dimension

Lecture 10: The four fundamental subspaces

Lecture 11: Matrix spaces; rank 1; small world graphs

Lecture 12: Graphs, networks, incidence matrices

Lecture 13: Quiz 1 review

Lecture 14: Orthogonal vectors and subspaces

Lecture 15: Projections onto subspaces

Lecture 16: Projection matrices and least squares

Lecture 17: Orthogonal matrices and Gram-Schmidt

Lecture 18: Properties of determinants

Lecture 19: Determinant formulas and cofactors

Lecture 20: Cramer's rule, inverse matrix, and volume

Lecture 21: Eigenvalues and eigenvectors

Lecture 22: Diagonalization and powers of A

Lecture 23: Differential equations and exp(At)

Lecture 24: Markov matrices; fourier series

Lecture 24b: Quiz 2 review

Lecture 25: Symmetric matrices and positive definiteness

Lecture 26: Complex matrices; fast fourier transform

Lecture 27: Positive definite matrices and minima

Lecture 28: Similar matrices and jordan form

Lecture 29: Singular value decomposition

Lecture 30: Linear transformations and their matrices

Lecture 31: Change of basis; image compression

Lecture 32: Quiz 3 review

Lecture 33: Left and right inverses; pseudoinverse

Lecture 34: Final course review