A Matricial Proof of the Symmetric Exchange Axiom for Eigenvalues of Principal Submatrices of a Complex Hermitian Matrix

In [C.R. Johnson, B. Kroschel, M. Omladič, Eigenvalue multiplicities in principal submatrices, Linear Algebra Appl. 390 (2004) 111-120] a result constraining the eigenvalues of principal submatrices of complex Hermitian matrices, based upon matroid theory, was given. Here we give a matricial proof of this result which also enables us to find a generalization of the original result.