Gilbert Strang

Lecture 01: The Geometry of Linear Equations

Lecture 02: Elimination with Matrices

Lecture 03: Multiplication and Inverse Matrices

Lecture 06: Column Space and Nullspace

Lecture 05: Transposes, Permutations, Spaces R^n

Lecture 04: Factorization into A = LU

Lecture 09: Independence, Basis, and Dimension

Lecture 07: Solving Ax = 0: Pivot Variables, Special Solutions

Lecture 10: The Four Fundamental Subspaces

Lecture 08: Solving Ax = b: Row Reduced Form R

Lecture 21: Eigenvalues and Eigenvectors

Lecture 22: Diagonalization and Powers of A

Lecture 14: Orthogonal Vectors and Subspaces

Lecture 11: Matrix Spaces; Rank 1; Small World Graphs

Lecture 15: Projections onto Subspaces

Lecture 12: Graphs, Networks, Incidence Matrices

Lecture 18: Properties of Determinants

Lecture 17: Orthogonal Matrices and Gram-Schmidt

Lecture 13: Quiz 1 Review

Lecture 16: Projection Matrices and Least Squares

Lecture 19: Determinant Formulas and Cofactors

Lecture 23: Differential Equations and exp(At)

Lecture 20: Cramer's Rule, Inverse Matrix, and Volume

Lecture 01: Difference Methods for Ordinary Differential Equations

Lecture 25: Symmetric Matrices and Positive Definiteness

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

Linear Algebra vs Calculus

Lecture 24B: Quiz 2 Review

Gil Strang's Introduction to Highlights of Calculus

Lecture 24: Markov Matrices; Fourier Series

Lecture 27: Positive Definite Matrices and Minima

Lecture 26: Complex Matrices; Fast Fourier Transform

Lecture 33: Left and Right Inverses; Pseudoinverse

Lecture 34: Final Course Review

Big Picture of Calculus

Lecture 01: Positive Definite Matrices K = A'CA

Lecture 32: Quiz 3 Review

Big Picture: Derivatives

Lecture 02: Finite Differences, Accuracy, Stability, Convergence

Lecture 14: Financial Mathematics / Black-Scholes Equation

The Exponential Function

Big Picture: Integrals

Max and Min and Second Derivative

Lecture 23: Calculus of Variations / Weak Form

Lecture 03: The One-way Wave Equation and CFL / von Neumann Stability

Lecture 15: Iterative Methods and Preconditioners

Lecture 28: Linear Programming and Duality