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 find expressions for many types of generalized inverses of an arbitrary square
complex matrix by using two representations given in [Benítez J. A new decomposition
for square matrices. Electron. J. Linear Algebra. ...
Let R be a ring and a, b is an element of R satisfy aba = a and bab = b. We characterize when ab - ba is invertible. This study is specialized when R has an involution and when b is the Moore-Penrose inverse of a.
In this work we study conditions for guaranteeing the nonnegativity of a discrete-time
singular control system. A first approach can be found in the literature for general systems, using the whole coefficient matrices. ...
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 {Am}
¿
m=1
be a sequence of complex group invertible matrices that converges to
A. We characterize when A is group invertible and {A
#
m}
¿
m=1
converges to A
#
in terms of the
canonical angles between ...
Hongwei, J.; Benítez López, Julio(ILAS–the International Linear Algebra Society, 2015-12)
In this paper, it is given equivalent conditions for the absorption laws in terms of the Moore-Penrose, group, core inverse, core inverse dual, {1}, {1,2}, {1,3}, and {1,4} inverses in rings. The results given here extend ...
[EN] In this paper, we recall and extend some tensor operations. Then, the generalized inverse of tensors is established by using tensor equations. Moreover, we investigate the leastsquares solutions of tensor equations. ...
The inverse eigenvalue problem and the associated optimal approximation problem for
Hermitian reflexive matrices with respect to a normal {k+1}-potent matrix are considered. First, we study the existence of the solutions ...