Eigenvalue algorithms

Cauchy’s spectral theorem for symmetric matrices, and hand-rolled power iteration and inverse iteration – two routes to a single eigenpair when the full spectrum isn’t needed.

Also: Gershgorin discs, Lanczos iteration for a few eigenpairs of a large sparse matrix, and the QR algorithm converging to the Schur form. An animation shows power iteration turning a vector onto the dominant eigenvector.

Cauchy’s spectral theorem: principal axes of a quadratic form

Cauchy's spectral theorem: principal axes of a quadratic form

Von Mises power iteration and Wielandt inverse iteration

Von Mises power iteration and Wielandt inverse iteration

Gershgorin discs

Gershgorin discs

Lanczos: a few eigenvalues of a very large matrix

Lanczos: a few eigenvalues of a very large matrix

The QR algorithm and the Schur form

The QR algorithm and the Schur form

Animated: power iteration turning a vector towards the dominant eigenvector

Animated: power iteration turning a vector towards the dominant eigenvector