These video lectures of Professor Gilbert Strang teaching 18.06 were recorded live in the Fall of 1999. Support for the video production was provided by the Lord Foundation of Massachusetts under a grant to the MIT Center for Advanced Educational Services.

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