# Bases of common eigenvectors

1. Apr 2, 2010

### hanch

Given a set of n<d commuting operators, either degenerate or non-degenerate, in a d-dimensional Hilbert space, is there an effective analytical method of finding an orthonormal basis composed of d eigenvectors common to all the operators in the set?
The operators are dxd complex square matrices, and the d-dimensional vectors in the desired orthonormal basis must be eigenvectors of all the operators. I was wondering if there is an efficient way to compute such vectors in a computer algebra system, such as Mathematica.

Last edited: Apr 2, 2010
2. Apr 2, 2010

### Landau

I don't know, but maybe http://www.math.rwth-aachen.de/mapleAnswers/html/368.html [Broken] helps.

Last edited by a moderator: May 4, 2017