A very short proof of Cauchy's interlace theorem for eigenvalues of Hermitian matrices

2005/02/18 by Steve Fisk · 5 citations
Mathematics · #math.CA

paper · pdf

published as Amer. Math. Monthly, Vol 112, No. 2, Feb. 2005, page 118 · 1 page

arxiv created 2005/02/18 · arxiv updated 2009/12/01

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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