Lecture 1: The Column Space of A Contains All Vectors Ax

Lecture 2: Multiplying and Factoring Matrices

3. Orthonormal Columns in Q Give Q'Q = I

5. Positive Definite and Semidefinite Matrices

6. Singular Value Decomposition (SVD)

7. Eckart-Young: The Closest Rank k Matrix to A

Lecture 8: Norms of Vectors and Matrices (18.065)

Lecture 9: Four Ways to Solve Least Squares Problems (18.065)

Lecture 10: Survey of Difficulties with Ax = b (18.065)

Lecture 11: Minimizing "x" Subject to Ax = b (18.065)

Lecture 12: Computing Eigenvalues and Singular Values (18.065)

Lecture 13: Randomized Matrix Multiplication (18.065)

Lecture 14: Low Rank Changes in A and Its Inverse (18.065)

Lecture 15: Matrices A(t) Depending on t, Derivative = dA/dt (18.065)

Lecture 16: Derivatives of Inverse and Singular Values (18.065)

Lecture 17: Rapidly Decreasing Singular Values (18.065)

Lecture 18: Counting Parameters in SVD, LU, QR, Saddle Points (18.065)

Lecture 19: Saddle Points Continued, Maxmin Principle (18.065)

Lecture 20: Definitions and Inequalities (18.065)