Projections and Idempotents in star-reducing Rings Involving the Moore-Penrose Inverse

Abstract

In [Comput. Math. Appl. 59 (2010) 764-778], Baksalary and Trenkler characterized some complex idempotent matrices of the form (I − P Q) † P (I − Q), (I − QP ) † (I − Q) and P (P + Q − QP ) † in terms of the column spaces and null spaces of P and Q, whereWe generalize these results from C n,n to any * -reducing rings.