A very short proof of Cauchy's interlace theorem for eigenvalues of Hermitian matrices
Classical Analysis and ODEs
2007-05-23 v1
Abstract
Cauchy's interlace theorem states that the characteristic polynomial of a symmetric matrix is interlaced by the characteristic polynomial of any principle submatrix. We prove this in two sentences using only the linearity of the determinant, and the fact that all eigenvalues of a symmetric matrix are real.
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@article{arxiv.math/0502408,
title = {A very short proof of Cauchy's interlace theorem for eigenvalues of Hermitian matrices},
author = {Steve Fisk},
journal= {arXiv preprint arXiv:math/0502408},
year = {2007}
}
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