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arXiv · 1206.3744

Generalization of Mirsky's theorem on diagonals and eigenvalues of matrices

Dragomir Z. Djokovic
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Abstract

Mirsky proved that, for the existence of a complex matrix with given eigenvalues and diagonal entries, the obvious necessary condition is also sufficient. We generalize this theorem to matrices over any field and provide a short proof. Moreover, we show that there is a unique companion-matrix-type solution for this problem.

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Dragomir Z. Djokovic. 2012-06-17. Generalization of Mirsky's theorem on diagonals and eigenvalues of matrices. https://doi.org/10.1016/j.laa.2012.06.040

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