Linear algebra #4: Eigendecomposition and singularvalue decomposition
Mike X Cohen, Neuroscientist, teacher, writer


1. What are eigenvalues and eigenvectors?
13:34 
2. Finding eigenvalues
15:42 
3. Shortcut for eigenvalues of a 2x2 matrix
2:04 
4. Code challenge: eigenvalues of diagonal and triangular matrices
5:59 
5. Code challenge: eigenvalues of random matrices
6:52 
6. Finding eigenvectors
13:13 
7. Diagonalization
10:30 
8. Matrix powers via diagonalization
16:10 
9. Eigenvectors of distinct eigenvalues
9:12 
10. Eigenvectors of repeated eigenvalues
12:15 
11. Eigendecomposition of symmetric matrices
14:31 
12. Eigendecomposition of singular matrices
4:19 
13. Generalized eigendecomposition
11:10 
14. Singular value decomposition (SVD)
13:19 
15. Code challenge: SVD vs. eigendecomposition for square symmetric matrices
12:53 
16. SVD and the four subspaces
8:08 
17. Spectral theory of matrices
12:57 
18. SVD for lowrank approximations
10:16 
19. Convert singular values to percent variance
11:36 
20. SVD, matrix inverse, and pseudoinverse
9:34 
21. Condition number of a matrix
8:19

About This Class
This class follows from linear algebra #13. You could start with this class if you feel comfortable with elementary linear algebra. If you are confused by the topics in this class, then it's probably best for you to go through earlier classes in this series.
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Officially I'm Dr. Michael X Cohen, but I prefer just "Mike" or "Mike X" or "the mysterious X." I'm a scientist because I believe that discovery and the drive to understand mysteries are among the most important drivers of progress in human civilization. And I believe in teaching because, well, because I really like teaching. I've been doing it my whole life. I teach "reallife" courses, online courses, university courses. I've written several books about neuroscience and data analysis, which...