Lecture Details

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