Systems of Differential Equations - Diagonalization and Jordan Canonical Form

Explore the concept of diagonalization and Jordan Canonical Form in systems of differential equations through this comprehensive video lecture. Learn when it's possible to perfectly diagonalize certain systems of linear differential equations and how to "block-diagonalize" more general cases. Dive into the computation of eigenvectors and generalized eigenvectors, and examine specific scenarios such as complex conjugate eigenvalues and repeated eigenvalues. Investigate a 3x3 degenerate matrix example and discover the fully general Jordan form for matrices. Gain valuable insights into advanced linear algebra concepts and their applications in differential equations.

A tale of two "A" matrices
When it's possible to diagonalize a matrix with eigenvectors
Computing eigenvectors and generalized eigenvectors
Case of complex conjugate eigenvalues
Case of repeated eigenvalues
3x3 degenerate matrix
Jordan canonical form for general matrix