This is a basic subject on matrix theory and linear algebra. Emphasis is given to topics that will be useful in other disciplines, including systems of equations, vector spaces, determinants, eigenvalues, similarity, and positive definite matrices.

 

Video Lectures

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.

Video Lectures Table

Lec #	Topics
1	The Geometry of Linear Equations
2	Elimination with Matrices
3	Multiplication and Inverse Matrices
4	Factorization into A = LU
5	Transposes, Permutations, Spaces R^n
6	Column Space and Nullspace
7	Solving Ax = 0: Pivot Variables, Special Solutions
8	Solving Ax = b: Row Reduced Form R
9	Independence, Basis, and Dimension
10	The Four Fundamental Subspaces
11	Matrix Spaces; Rank 1; Small World Graphs
12	Graphs, Networks, Incidence Matrices
13	Quiz 1 Review
14	Orthogonal Vectors and Subspaces
15	Projections onto Subspaces
16	Projection Matrices and Least Squares
17	Orthogonal Matrices and Gram-Schmidt
18	Properties of Determinants
19	Determinant Formulas and Cofactors
20	Cramer's Rule, Inverse Matrix, and Volume
21	Eigenvalues and Eigenvectors
22	Diagonalization and Powers of A
23	Differential Equations and exp(At)
24	Markov Matrices; Fourier Series
24b	Quiz 2 Review
25	Symmetric Matrices and Positive Definiteness
26	Complex Matrices; Fast Fourier Transform
27	Positive Definite Matrices and Minima
28	Similar Matrices and Jordan Form
29	Singular Value Decomposition
30	Linear Transformations and Their Matrices
31	Change of Basis; Image Compression
32	Quiz 3 Review
33	Left and Right Inverses; Pseudoinverse
34	Final Course Review