We give a very short proof of the main result of J. Benitez, A new decomposition for square matrices, Electron. J. Linear Algebra 20 (2010) 207-225. Also, we present some consequences of this result. (C) 2012 Elsevier Inc. ...

We derive a very short expression for the group inverse of a(1) + ... + a(n) when a(1), ... , a(n) are elements in an algebra having group inverse and satisfying a(i)a(j) = 0 for i < j. We apply this formula in order to ...

Liu, Xiaoji; Wu, Lingling; Benítez López, Julio(ILAS–the International Linear Algebra Society, 2011-05)

[EN] In this paper, some formulas are found for the group inverse of aP | bQ, where P and Q are two nonzero group invertible complex matrices satisfying certain conditions and a, b nonzero complex numbers.