# Linear Algebra with Gilbert Strang

### Course Description

18.06 Linear Algebra 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.

Gilbert Strang, 18.06 Linear Algebra, Spring 2005. (MIT OpenCourseWare: Massachusetts Institute of Technology), http://ocw.mit.edu/OcwWeb/Mathematics/18-06Spring-2005/Cours... (Accessed August 07, 2008). License: Creative commons BY-NC-SA
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### Video Lectures & Study Materials

Visit the official course website for more study materials: http://ocw.mit.edu/courses/mathematics/18-06-linear-algebra-spring-2010/

# Lecture Play Lecture
I. Solving Linear Equations
1 The Geometry of Linear Equations (39:52) Play Video
2 Elimination with Matrices (49:48) Play Video
3 Multiplication and Inverse Matrices (49:31) Play Video
4 Factorization into A = LU (50:13) Play Video
5 Transposes, Permutations, Spaces Rn (47:41) Play Video
II. Vector Spaces and Subspaces
6 Column Space and Nullspace (46:01) Play Video
7 Solving Ax = 0: Pivot Variables, Special Solutions (43:19) Play Video
8 Solving Ax = b: Row Reduced Form R (47:12) Play Video
9 Independence, Basis, and Dimension (50:07) Play Video
10 The Four Fundamental Subspaces (49:19) Play Video
11 Matrix Spaces; Rank 1; Small World Graphs (46:02) Play Video
12 Graphs, Networks, Incidence Matrices (47:56) Play Video
13 Quiz 1 Review (47:46) Play Video
III. Orthogonality
14 Orthogonal Vectors and Subspaces (49:51) Play Video
15 Projections onto Subspaces (48:53) Play Video
16 Projection Matrices and Least Squares (48:05) Play Video
17 Orthogonal Matrices and Gram-Schmidt (49:24) Play Video
IV. Determinants
18 Properties of Determinants (49:14) Play Video
19 Determinant Formulas and Cofactors (53:21) Play Video
20 Cramer's Rule, Inverse Matrix, and Volume (51:00) Play Video
V. Eigenvalues and Eigenvectors
21 Eigenvalues and Eigenvectors (51:21) Play Video
22 Diagonalization and Powers of A (51:55) Play Video
23 Differential Equations and exp(At) (51:08) Play Video
24 Markov Matrices; Fourier Series (51:14) Play Video
25 Quiz 2 Review (48:21) Play Video
26 Symmetric Matrices and Positive Definiteness (43:56) Play Video
27 Complex Matrices; Fast Fourier Transform (47:51) Play Video
28 Positive Definite Matrices and Minima (50:39) Play Video
29 Similar Matrices and Jordan Form (45:57) Play Video
30 Singular Value Decomposition (40:30) Play Video
VI. Linear Transformations
31 Linear Transformations and Their Matrices (49:30) Play Video
32 Change of Basis; Image Compression (50:16) Play Video
33 Quiz 3 Review (47:03) Play Video
34 Left and Right Inverses; Pseudoinverse (41:52) Play Video
35 Final Course Review (43:25) Play Video