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For , let be a hermitian matrix (for instance a symmetric matrix of all entries are real numbers).
Then for every principal submatrix , obtained by deleting the th column and the th row from , for some , the eigenvalues of interlace the eigenvalues of , in that
Suk-Geun Hwang, Cauchy’s Interlace Theorem for Eigenvalues of Hermitian Matrices, The American Mathematical Monthly Vol. 111, No. 2 (Feb., 2004), pp. 157-159 (jstor:4145217)
Steve Fisk, A very short proof of Cauchy’s interlace theorem for eigenvalues of Hermitian matrices (arXiv:math/0502408)
See also:
Wikipedia, Cauchy interlacing theorem
Wikipedia, Poincaré separation theorem
Last revised on April 29, 2021 at 09:48:30. See the history of this page for a list of all contributions to it.