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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.
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Susana Furtado, , Congruence and <em>A<sup>-1</sup>A<sup>*</sup></em>. Port. Math. 64 (2007), no. 2, pp. 237–251DOI 10.4171/PM/1785