# Glossary for Linear Algebra + Quick Tips

1. Oct 18, 2005

### Greg Bernhardt

Author: Gilbert Strang from MIT

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• ###### linear_nutshell.pdf
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2. Oct 20, 2005

### FredGarvin

Thanks Greg! That couldn't have come at a better time for me!

3. Feb 9, 2006

### arab mathematical

Thank you, for this subject

4. Mar 2, 2006

### Jenga

And in case you haven't checked it out already, there's also the accompanying OpenCourseware site. The video lectures on the page are pretty good, although you may want to download the full ~100 mb file to reduce stuttering if your connection is not up to it.

5. Oct 9, 2010

### Staff: Mentor

W. Gilbert Strang's lectures on Linear Algebra are available on-line

http://ocw.mit.edu/courses/mathematics/18-06-linear-algebra-spring-2010/video-lectures/

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 Rn
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 - Symmetric Matrices and Positive Definiteness
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

Also on Youtube - starting with Lecture 1 (Spring 2005) -

Last edited by a moderator: Sep 25, 2014