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I do not know about eigenvectors, but for the eigenvalues this is a special case of Deligne-Simpson Problem. It was completely solved by Crawley-Boevey about 10 years ago using quivers. For details, see my answer herehere and references therein.

I do not know about eigenvectors, but for the eigenvalues this is a special case of Deligne-Simpson Problem. It was completely solved by Crawley-Boevey about 10 years ago using quivers. For details, see my answer here and references therein.

I do not know about eigenvectors, but for the eigenvalues this is a special case of Deligne-Simpson Problem. It was completely solved by Crawley-Boevey about 10 years ago using quivers. For details, see my answer here and references therein.

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Misha
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I do not know about eigenvectors, but for the eigenvalues this is a special case of Deligne-Simpson Problem. It was completely solved by Crawley-Boevey about 10 years ago using quivers. For details, see my answer here and references therein.