The minus partial order and the shorted matrix

Abstract

The minus partial order was defined by Hartwig [6], weakening the conditions of the star partial order of Drazin [5]. Several new properties of the minus partial order are established. The minus partial order is used to redefine the shorted matrix [15, 17] and to define the infimum A ∧ B and the supremum A ∨ B of a pair A, B of matrices of the same order. The definition of the shorted matrix given here is similar to the Krein-Anderson-Trapp definition of the shorted positive operator.