Linear algebra #4: Eigendecomposition and singular-value decomposition

Mike X Cohen, Neuroscientist, teacher, writer

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21 Videos (3h 43m)
    • What are eigenvalues and eigenvectors?

      13:34
    • Finding eigenvalues

      15:42
    • Shortcut for eigenvalues of a 2x2 matrix

      2:04
    • Code challenge: eigenvalues of diagonal and triangular matrices

      5:59
    • Code challenge: eigenvalues of random matrices

      6:52
    • Finding eigenvectors

      13:13
    • Diagonalization

      10:30
    • Matrix powers via diagonalization

      16:10
    • Eigenvectors of distinct eigenvalues

      9:12
    • Eigenvectors of repeated eigenvalues

      12:15
    • Eigendecomposition of symmetric matrices

      14:31
    • Eigendecomposition of singular matrices

      4:19
    • Generalized eigendecomposition

      11:10
    • Singular value decomposition (SVD)

      13:19
    • Code challenge: SVD vs. eigendecomposition for square symmetric matrices

      12:53
    • SVD and the four subspaces

      8:08
    • Spectral theory of matrices

      12:57
    • SVD for low-rank approximations

      10:16
    • Convert singular values to percent variance

      11:36
    • SVD, matrix inverse, and pseudoinverse

      9:34
    • Condition number of a matrix

      8:19

About This Class

This class follows from linear algebra #1-3. 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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Mike X Cohen

Neuroscientist, teacher, writer

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 "real-life" courses, online courses, university courses. I've written several books about neuroscience and data analysis, which...

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