Further results on generalized and hypergeneralized projectors

Abstract The notions of generalized and hypergeneralized projectors, introduced by Gros and Trenkler [J. Gro s , J. Trenkler, Generalized and hypergeneralized projectors, Linear Algebra Appl. 264 (1997) 463–474], are revisited. On the one hand, the present paper provides several new characterizations of these sets, and, on the other, the properties of generalized and hypergeneralized projectors related to various matrix partial orderings are considered. Moreover, the paper demonstrates the usefulness, in studying the properties of generalized and hypergeneralized projectors, of the representation of complex matrices given in Corollary 6 by Hartwig and Spindelbock [R.E. Hartwig, K. Spindelbock, Matrices for which A∗ and A† commute, Linear and Multilinear Algebra 14 (1984) 241-256].

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