Glossary for Linear Algebra + Quick Tips

[Greg Bernhardt]

Author: Gilbert Strang from MIT

 

[FredGarvin]

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

 

[arab mathematical]

Thank you, for this subject

 

[Jenga]

And in case you haven't checked it out already, there's also the accompanying http://ocw.mit.edu/OcwWeb/Mathematics/18-06Spring-2005/CourseHome/index.htm". 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.

 

[Astronuc]

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) -