SPEAKER: Pedro Patrício (CMAT)

DATE: 9 February 2023, 14h30m    

VENUE: Sala de Seminários do DMAT, Campus de Gualtar

ONLINE:  https://videoconf-colibri.zoom.us/j/93344876599?pwd=ejkrZ3FpYkh0NE1YV3NCdGFMOGw3QT09

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.