# (MIT 18.06) Introduction to Linear Algebra [Spring 2005]

## References
* [Video Lectures](https://www.youtube.com/playlist?list=PL49CF3715CB9EF31D)
* [Course Website](https://ocw.mit.edu/courses/mathematics/18-06-linear-algebra-spring-2010/)

## Info
- MIT, Gilbert Strang

## Content
1. The Geometry Of Linear Equations
2. Elimination With Matrices
3. Multiplication and Inverse Matrices
4. Factorization into A=LU
5. Transpose, Permutations, Spaces R^n
6. Column Space and Nullspace
7. Solving Ax=0: Pivot Variables, Special Solutions
8. Solving Ax=b: Row Reduces Form
9. Independence, Basis, and Dimensions
10. The Four Fundamental Spaces
11. Matrix Spaces; Rank 1;Small World Graphs
12. Graphs, Networks, Incidence Matrices
13. Orthogonal Vectors ann Subspaces
14. Projections onto Subspaces
15. Projection Matrices and Least Squares
16. Orthogonal Matrices and GramSchmidt
17. Properties of Determinants
18. Determinant Formulas and Cofactors
19. Cramers Rule, Inverse Matrix, and Volume
20. Eigenvalues and Eigenvectors
21. Diagonalization and Power of A
22. Differential Equations and exp(At)
23. Markov Matrices; Fourier Series
24. Symmetric Matrices and Positive Definitness
25. Complex Matrices; Fast Fourier Transform
26. Positive Definite Matrices and Minima
27. Similar Matrices and Jordan Form
28. Singular Value Decomposition
29. Linear Transformations and Their Matrices
30. change of basis
31. Left and Rite Inverses; Pseudoinverse