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Systems of Differential Equations - Diagonalization and Jordan Canonical Form

Steve Brunton via YouTube

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This course explains when systems of linear differential equations can be diagonalized and how generalized eigenvectors produce Jordan canonical form in the general case, including repeated and complex conjugate eigenvalues.

Syllabus

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

Taught by

Steve Brunton

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