Can Commuting Operators in a Hilbert Space Share a Common Set of Eigenvectors?

[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.

 

[Landau]

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