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Projections and Idempotents in star-reducing Rings Involving the Moore-Penrose Inverse (1307.5528v1)
Published 21 Jul 2013 in math.RA
Abstract: In [Comput. Math. Appl. 59 (2010) 764-778], Baksalary and Trenkler characterized some complex idempotent matrices of the form $(I-PQ){\dag}P(I-Q)$, $(I-QP){\dag}(I-Q)$ and $P(P+Q-QP){\dag}$ in terms of the column spaces and null spaces of $P$ and $Q$, where $P, Q\in \mathbb{C}{\textsf{OP}}_n = {L\in \mathbb{C}{n,n}\ |\ L2 = L = L*}$. We generalize these results from $\mathbb{C}{n,n}$ to any *-reducing rings.