The Eigenvalues of Complementary Principal Submatrices of a Positive Definite Matrix

Abstract

Let C be an n-square Hermitian matrix, presented in partitioned form aswhere A is a-square and B is b-square. Let denote the eigenvalues of C, A, B, respectively. In a recent paper [10] the following inequality was established:1.1if1.2This inequality is a simplification and a sharpening of an inequality established earlier in [6], and is a wide generalization of an inequality of Aronszajn [4].