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

By S. Fisk. 2005

71 citations recorded by the source corpus.

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.

Subfields: Algebra and Number Theory, Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/e8602b435ab2fcf14ae2e282df05b681ee8ea320

Citations in the corpus

• Seventy years of Salem numbers (2014, unknown): “Theorem 6 (Cauchy’s Interlacing Theorem; for a proof see for instance [42]).”