Systems of Differential Equations: Diagonalization and Jordan Canonical Form

It is only possible to perfectly diagonalize certain systems of linear differential equations. For the more general cases, it is possible to "block-diagonalize" the system into what is known as Jordan Canonical Form. This video explores these various options and derives the fully general Jordan form. Playlist: https://www.youtube.com/playlist?list=PLMrJAkhIeNNTYaOnVI3QpH7jgULnAmvPA Course Website: http://faculty.washington.edu/sbrunton/me564/ @eigensteve on Twitter eigensteve.com databookuw.com This video was produced at the University of Washington %%% CHAPTERS %%% 0:00 A tale of two "A" matrices 1:47 When it's possible to diagonalize a matrix with eigenvectors 6:15 Computing eigenvectors and generalized eigenvectors 20:03 Case of complex conjugate eigenvalues 23:10 Case of repeated eigenvalues 25:35 3x3 degenerate matrix 29:37 Jordan canonical form for general matrix