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18.06 Linear Algebra

18.06 Linear Algebra (Spring 2010, MIT OCW). This consists of 34 video lectures given by Professor Gilbert Strang, 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. (from ocw.mit.edu)

01. The geometry of linear equations 19. Determinant formulas and cofactors
02. Elimination with matrices 20. Cramer's rule, inverse matrix, and volume
03. Multiplication and inverse matrices 21. Eigenvalues and eigenvectors
04. Factorization into A = LU 22. Diagonalization and powers of A
05. Transposes, permutations, spaces Rn 23. Differential equations and exp(At)
06. Column space and nullspace 24. Markov matrices; Fourier series
07. Solving Ax = 0: pivot variables, special solutions 24b. Quiz 2 review
08. Solving Ax = b: row reduced form R 25. Symmetric matrices and positive definiteness
09. Independence, basis, and dimension 26. Complex matrices; fast Fourier transform
10. The four fundamental subspaces 27. Positive definite matrices and minima
11. Matrix spaces; rank 1; small world graphs 28. Similar matrices and Jordan form
12. Graphs, networks, incidence matrices 29. Singular value decomposition (!viewing size)
13. Quiz 1 review 30. Linear transformations and their matrices
14. Orthogonal vectors and subspaces 31. Change of basis; image compression
15. Projections onto subspaces 32. Quiz 3 review
16. Projection matrices and least squares 33. Left and right inverses; pseudoinverse
17. Orthogonal matrices and Gram-Schmidt 34. Final course review
18. Properties of determinants

References
18.06 Linear Algebra
Instructors: Prof. Gilbert Strang. Exams and Solutions. Subtitles/Transcript. Assignments and Solutions. This is a basic subject on matrix theory and linear algebra.