18.06SC Linear Algebra

MIT OCW - 18.06SC Linear Algebra (Fall 2011). Taught by Professor Gilbert Strang, this course covers matrix theory and linear algebra, emphasizing topics useful in other disciplines such as physics, economics and social sciences, natural sciences, and engineering. This course has been designed for independent study. It provides everything you will need to understand the concepts covered in the course. The materials include: a complete set of lecture videos, summary notes, problem solving videos, and a full set of exams and solutions.
(from ocw.mit.edu)

An Overview of Key Ideas

Professor Strang recommends this video from his Computational Science and Engineering I course (18.085) as an overview of the basics of linear algebra.


References
An Overview of Key Ideas
Professor Strang recommends this video from his Computational Science and Engineering I course as an overview of the basics of linear algebra. Lecture Video and Summary. Suggested Reading. Problem Solving Video.

Go to Linear Algebra Home or watch other lectures:

I. Ax=b and the Four Subspaces 19. Properties of Determinants
01. The Geometry of Linear Equations 20. Determinant Formulas and Cofactors
02. An Overview of Key Ideas 21. Cramer's Rule, Inverse Matrix and Volume
03. Elimination with Matrices 22. Eigenvalues and Eigenvectors
04. Multiplication and Inverse Matrices 23. Diagonalization and Powers of A
05. Factorization into A = LU 24. Differential Equations and exp(At)
06. Transposes, Permutations, Vector Spaces 25. Markov Matrices; Fourier series
07. Column Space and Nullspace 26. Exam 2 Review
08. Solving Ax = 0: Pivot Variables, Special Solutions III. Positive Definite Matrices and Applications
09. Solving Ax = b: Row Reduced form R 27. Symmetric Matrices and Positive Definiteness
10. Independence, Basis and Dimension 28. Complex Matrices; Fast Fourier Transform
11. The Four Fundamental Subspaces 29. Positive Definite Matrices and Minima
12. Matrix Spaces; Rank 1; Small World Graphs 30. Similar Matrices and Jordan Form
13. Graphs, Networks, Incidence Matrices 31. Singular Value Decomposition
14. Exam 1 Review 32. Linear Transformations and their Matrices
II. Least Squares, Determinants and Eigenvalues 33. Change of Basis; Image Compression
15. Orthogonal Vectors and Subspaces 34. Left and Right Inverses; Pseudoinverse
16. Projections onto Subspaces 35. Exam 3 Review
17. Projection Matrices and Least Squares 36. Final Course Review
18. Orthogonal Matrices and Gram-Schmidt