[EN] In this work, given a unital Banach algebra A and a \in A such that a has a Moore-Penrose inverse a^+, it will be characterized when a^+ a - a a^+ is invertible. A particular subset of this class of objects wil also ...
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 ...
This paper gives simple proofs of Sylvester (` = 2) and Frobenius
(` = 3) inequalities. Moreover, a new sufficient condition for the
equality of the Frobenius inequality is provided. In addition, an extension
for ` > 3 ...
[EN] The purpose of this paper is to introduce a new generalized inverse, called DMP inverse, associated with a square complex matrix using its Drazin and Moore-Penrose inverses. DMP inverse extends the notion of core ...
Malik, Saroj B.; Thome, Néstor(National Library of Serbia, 2017)
[EN] For two given Hilbert spaces H and K and a given bounded linear operator A is an element of L(H, K) having closed range, it is well known that the Moore-Penrose inverse of A is a reflexive g-inverse G is an element ...
[EN] Let R be a unital ring with involution. In Section 2, for given two core invertible elements a, b. R, we investigate mainly the absorption law for the core inverse in virtue of the equality of the projections aa and ...
The well-known classes of EP matrices and normal matrices are de-
fined by the matrices that commute with their Moore-Penrose inverse
and with their conjugate transpose, respectively. This paper investigates
the class ...
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 ...
[EN] The space of n x n complex matrices with the star partial order is considered in the first part of this paper. The class of EP matrices is analyzed and several properties related to this order are given. In addition, ...