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
Lecture #24.5 : Quiz 2 Review
Lecture #24 : Markov Matrices; Fourier Series
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