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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.

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.

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