Linear Algebra

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 24a: 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

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