index.md

MIT OCW : Linear Algebra

1. The Geometry of Linear Equations
2. Elimination with Matrice
3. Multiplication and Inverse Matrices
4. Factorization into A = LU
5. Transposes, Permutations, Vector Spaces
6. Column Space and Nullspace
7. Ax=0: Pivot variables, special solutions
8. Ax=b: Row Reduced Form R
9. Independence, Basis and Dimension
10. The Four Fundamental Subspaces
11. Graphs, Networks, Incidence Matrics
12. Orthogonal Vectors and Subspaces
13. Projections onto Subspaces
14. Projection Matrices and Least Squares
15. Orthogonal Matrices and Gram-Schmidt
16. Properties of Determinants
17. Determinant Formulas and Cofactors
18. Cramer's Rule, Inverse Matrix and Volume
19. Eigenvalues and Eigenvectors
20. Diagonalization and Powers of A
21. Differential Equations and exp(At)
22. Markov Matrices and Fourier Series