Congruence and <em>A^-1A^*</em>

Abstract

A canonical form under congruence for nonsingular complex matrices may be deduced from the canonical pair form for Hermitian matrices in a straightforward way. This allows the study of A-1A* and what it says about the congruence class of A. In turn, alternate congruential forms may be given along with a further generalization of Sylvester's law of inertia and an application to C-S equivalence.