Speaker: Roger A. Horn

Title: Canonical Forms for Congruence and *Congruence of Complex Matrices

Abstract: Recent work has produced sets of simple canonical matrices for
both congruence (A -> S^TAS) and *congruence (A -> S^*AS) of complex
matrices, together with algorithms to compute them. The theory for these
two equivalence relations is an analog of the classical Jordan Canonical
Form, for which the equivalence relation is similarity, but it is
different in very interesting ways.  Applications include a new theory
of canonical pairs for Hermitian/Hermitian and symmetric/skew-symmetric
pairs of complex matrices, characterization of matrices with positive
semidefinite Hermitian part, stability of canonical forms under
perturbation.