Congruence and \(A^{-1}A^*\) (Q2456043)

It is known that a canonical form under congruence for nonsingular complex matrices may be deduced from the canonical pair form for Hermitian matrices in a straightforward way. The authors study \(A^{-1}A^*\) and what it says about the congruence class of \(A\). In turn, alternate congruential form may be given along with a further generalization of Sylvester's law of inertia and an application to C-S equivalence.