2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/63420We present a class of symplectic matrices which transform by similarity given $2n\times 2n$ -dimensional matrix into Bunse-Gerstner form. If the given matrix is skew-Hamiltonian, the transformation gives a solution of an antisymmetric Riccati matrix equation, resulting from optimal control of linear systems.submitted to ELA for publicationRings and Algebras15A24, 15A18, 35G05text