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

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

2005-02-18

arxiv.org/abs/math/0502408v1

Amer. Math. Monthly, Vol 112, No. 2, Feb. 2005, page 118

Mathematics

Classical Analysis and ODEs

1 page

Scientific paper

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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