A very short proof of Cauchy's interlace theorem for eigenvalues of Hermitian matrices
Steve Fisk · arXiv (Cornell University) · 2005
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.