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arXiv · 0904.0734

Short proofs of theorems of Mirsky and Horn on diagonals and eigenvalues of matrices

Eric A. Carlen·Elliott H. Lieb
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Abstract

A theorem of Mirsky provides necessary and sufficient conditions for the existence of an N-square complex matrix with prescribed diagonal entries and prescribed eigenvalues. We give a simple inductive proof of this theorem.

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Eric A. Carlen, Elliott H. Lieb. 2011-05-12. Short proofs of theorems of Mirsky and Horn on diagonals and eigenvalues of matrices. https://arxiv.org/abs/0904.0734

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