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 ...
Lebtahi Ep-Kadi-Hahifi, Leila; Romero Martínez, José Oscar; Thome, Néstor(Elsevier, 2012-01-15)
Recently, situations where a matrix coincides with some of its powers have been studied. This kind of matrices is related to the generalized inverse matrices. On the other hand, it is possible to introduce another class ...
In this paper, we use the Drazin inverse to derive some new equivalences of the reverse order law for the group inverse in unitary rings. Moreover, if the ring has an involution, we present more equivalences when both ...
Catral, M.; Lebtahi Ep-Kadi-Hahifi, Leila; Stuart, Jeffrey; Thome, Néstor(Elsevier, 2014-11-15)
Let R is an element of C-nxn be a {k}-involutory matrix (that is, R-k = I-n) for some integer k >= 2, and let s be a nonnegative integer. A matrix A is an element of C-nxn is called an {R,s + 1, k}-potent matrix if A ...
Benítez López, Julio; Cvetkovic-Ilic, D.; Liu, X.(Duke University Press, 2014)
[EN] Let {a_n} be a sequence of group invertible elements of a unital C* algebra A that converges to a. We present some equivalent conditions for the group invertibility of a and for the convergence of {a^#_n} to a#.
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.
Herrero Debón, Alicia; Ramirez, Francisco J.; Thome, Néstor(Elsevier, 2013-02-15)
This paper deals with nonnegativity of matrices and their group or Drazin inverses. Firstly, the nonnegativity of a square matrix A, its group inverse A# and its group projector AA# is used to define different sets for ...
Benítez López, Julio; Boasso, Enrico(University of Wyoming Libraries, 2016)
[EN] Several properties of the inverse along an element are studied in the context of unitary rings. New characterizations of the existence of this inverse are proved. Moreover, the set of all invertible elements along a ...