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Listar por autor "Liu, Xiaoji"

Mostrando ítems 1-10 de 10

A short proof of a matrix decomposition with applications

Benítez López, Julio; Liu, Xiaoji (Elsevier, 2013-02-01)

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. ...
Additive results for the group inverse in an algebra with applications to block operators

Benítez López, Julio; Liu, Xiaoji; Zhu, Tongping (Taylor & Francis, 2011)

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 ...
Further results on the reverse order law for the group inverse in rings

Liu, Xiaoji; Zhang, Miao; Benítez López, Julio (Elsevier, 2014-02-25)

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 ...
Invertibility in rings of the commutator ab-ba, where aba=a and bab=b

Benítez López, Julio; Liu, Xiaoji; Rakocevic, Vladimir (Taylor & Francis, 2012)

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.
On linear combinations of generalized involutive matrices

Liu, Xiaoji; Wu, Lingling; Benítez López, Julio (Taylor & Francis, 2011)

Let X(dagger) denotes the Moore-Penrose pseudoinverse of a matrix X. We study a number of situations when (aA + bB)(dagger) = aA + bB provided a, b is an element of C\{0} and A, B are n x n complex matrices such that ...
On nonsingularity of combinations of two group invertible matrices and two tripotent matrices

Liu, Xiaoji; Wu, Shuxia; Benítez López, Julio (Taylor & Francis, 2011)

Let T(1) and T(2) be two n x n tripotent matrices and c(1), c(2) two nonzero complex numbers. We mainly study the nonsingularity of combinations T = c(1)T(1) + c(2)T(2) - c(3)T(1)T(2) of two tripotent matrices T(1) and ...
On the group inverse of linear combinations of two group invertible matrices

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.
Simultaneous decomposition of two EP matrices with applications

Benítez López, Julio; Liu, Xiaoji (ILAS–the International Linear Algebra Society, 2014-06)

[EN] We find a simple canonical form for EP complex matrices A and B under simultaneous unitary equivalence.
The generalized inverses of tensors and an application to linear models

Jin, Hongwei; Bai, Minru; Benítez López, Julio; Liu, Xiaoji (Elsevier, 2017)

[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 spectrum of matrices depending on two idempotents

Liu, Xiaoji; Benítez López, Julio (Elsevier, 2011-10)

Let P and Q be two complex matrices satisfying P2=P and Q 2=Q. For a,b nonzero complex numbers such that aP+bQ is diagonalizable, we relate the spectrum of aP+bQ to the spectra of P-Q, PQ, PQP and PQ-QP. © 2011 Elsevier ...