JournalspmVol. 64 / No. 2DOI 10.4171/pm/1785

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

  • Susana Furtado

    Universidade do Porto, Portugal
  • College of William and Mary, Williamsburg, United States
Congruence and <em>A<sup>-1</sup>A<sup>*</sup></em> cover

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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.