On linear combinations of two commuting hypergeneralized projectors
The concept of a hypergeneralized projector as a matrix H satisfying H 2 = H  , where H  denotes the MoorePenrose inverse of H , was introduced by Groand Trenkler in [J. Gro, G. Trenkler, Generalized and hypergeneralized projectors, Linear Algebra Appl. 264 (1997) 463474]. Generalizing substantially preliminary observations given therein, Baksalary etal.in [J.K. Baksalary, O.M. Baksalary, J. Gro, On some linear combinations of hypergeneralized projectors, Linear Algebra Appl. 413 (2006) 264273] characterized some situations in which a linear combination c 1 H 1 + c 2 H 2 , where c1,c2?C c 1 , c 2 ? C and H 1 , H 2 are hypergeneralized projectors such that H 1 H 2 = ? 1 H 1 2 + ? 2 H 2 2 = H 2 H 1 for some ?1,?2?C ? 1 , ? 2 ? C , inherits the hypergenerality property. In the present paper, the problem considered in the latter paper is revisited and solved completely under the essentially weaker assumption that H 1 H 2 = H 2 H 1 .
moorepenrose inverse partitioned matrix ep matrix diagonalizability