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 #24.5 : 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