SPEAKER: Pedro Patrício (CMAT)
DATE: 9 February 2023, 14h30m
VENUE: Sala de Seminários do DMAT, Campus de Gualtar
TITLE: Group inverses: decompositions, products and sums
ABSTRACT: The study of the group inverse of a product of matrices is not new, and was used to characterize de group inverse of a companion matrix (Puystjens, Hartwig, LAMA '97). One may use Jacobson's lemma to provide a simpler characterization. This lemma has generalized invertibility versions, which we will briefly address. Our goal is to characterize the group inverse of a product, as well as to derive an expression of such a group inverse that does not rely on the knowledge of von Neumann regularity of the product.