How to calculate eigenvalues using QR method?

Question

How can I get eigenvalues of matrix using Apache Commons Math? I know there is 2 classes EigenDecomposition and QRDecomposition, but how to combine them to get eigenvalues?

Answer 1

Why combine them? QR can give you eigenvalues:

http://en.wikipedia.org/wiki/QR_algorithm

Answer 2

You seem to confuse the QR decomposition with the QR eigenvalue algorithm.

The QR decomposition cannot give you the eigenvalues of a matrix, but it can be used as a component to a more complex algorithm that produce eigenvalues and eigenvectors.

http://en.wikipedia.org/wiki/QR_algorithm

http://en.wikipedia.org/wiki/QR_decomposition