Canonical forms for complex matrix congruence and \(^{*}\)-congruence (Q2496663)

The authors show that each square complex matrix is congruent to a direct sum of canonical matrices of three types that they describe. A similar statement holds for \(^\star\)-congruence. The authors also find canonical pairs for simultaneous congruence of pairs of complex symmetric and skew-symmetric matrices. Their proof provides explicit algorithms to compute all blocks and parameters in the canonical forms.