Results 51 to 60 of about 28,414 (283)

Drazin-Moore-Penrose invertibility in rings [PDF]

, 2004
Characterizations are given for elements in an arbitrary ring with involution, having a group inverse and a Moore-Penrose inverse that are equal and the difference between these elements and EP-elements is explained.
Ben-Israel, Bhaskara Rao, Campbell, Cohn, Drazin, Greub, Hartwig, Hartwig, Hartwig, Hartwig, Jacobson, Katz, Koliha, Lam, Lesnjak, Moore, Patrı́cio, Patrı́cio, Patrı́cio, Pedro Patrı́cio, Penrose, Puystjens, Puystjens, Puystjens, Puystjens, Robinson, Robinson, Roland Puystjens, Schwerdtfeger, Urquhart   +29 more
core   +2 more sources

On mixed-type reverse-order laws for the Moore-Penrose inverse of a matrix product

International Journal of Mathematics and Mathematical Sciences, 2004
Some mixed-type reverse-order laws for the Moore-Penrose inverse of a matrix product are established. Necessary and sufficient conditions for these laws to hold are found by the matrix rank method.
Yongge Tian
doaj   +1 more source

∗-Regularity in the ring of matrices over the ring of integers modulo 𝑛 [PDF]

Songklanakarin Journal of Science and Technology (SJST), 2023
For any positive integer 𝑛 ≥ 2, we give necessary and sufficient conditions of the existence of the Moore-Penrose inverse of any square matrix over the ring of integers modulo 𝑛.
Wannisa Apairat, Sompong Chuysurichay
doaj  

Efficient Predefined-Time Adaptive Neural Networks for Computing Time-Varying Tensor Moore–Penrose Inverse

IEEE Transactions on Neural Networks and Learning Systems
This article proposes predefined-time adaptive neural network (PTANN) and event-triggered PTANN (ET-PTANN) models to efficiently compute the time-varying tensor Moore–Penrose (MP) inverse.
Zhaohui Qi, Yingqiang Ning, Lin Xiao, Zidong Wang, Yongjun He   +4 more
semanticscholar   +1 more source

On polynomial EPr matrices

International Journal of Mathematics and Mathematical Sciences, 1992
This paper gives a characterization of EPr-λ-matrices. Necessary and sufficient conditions are determined for (i) the Moore-Penrose inverse of an EPr-λ-matrix to be an EPr-λ-matrix and (ii) Moore-Penrose inverse of the product of EPr-λ-matrices to be an ...
Ar. Meenakshi, N. Anandam
doaj   +1 more source

The Moore–Penrose inverse of a factorization

Linear Algebra and its Applications, 2003
AbstractIn this paper, we consider the product of matrices PAQ, where A is von Neumann regular and there exist P′ and Q′ such that P′PA=A=AQQ′. We give necessary and sufficient conditions in order to PAQ be Moore–Penrose invertible, extending known characterizations. Finally, an application is given to matrices over separative regular rings.
openaire   +3 more sources

Computing generalized inverses using LU factorization of matrix product

, 2011
An algorithm for computing {2, 3}, {2, 4}, {1, 2, 3}, {1, 2, 4} -inverses and the Moore-Penrose inverse of a given rational matrix A is established. Classes A(2, 3)s and A(2, 4)s are characterized in terms of matrix products (R*A)+R* and T*(AT*)+, where ...
Ben-Israel A., Campbell S. L., Chen L., Courrieu P., Lovass Nagy V., Milan B. Tasić, Predrag S. Stanimirović, Rao C. R., Stanimirović P. S., Stanimirović P. S., Wang G., Wolfram S.   +11 more
core   +1 more source

Solving reduced biquaternion matrices equation $ \sum\limits_{i = 1}^{k}A_iXB_i = C $ with special structure based on semi-tensor product of matrices

AIMS Mathematics, 2022
In this paper, we propose a real vector representation of reduced quaternion matrix and study its properties. By using this real vector representation, Moore-Penrose inverse, and semi-tensor product of matrices, we study some kinds of solutions of ...
Wenxv Ding, Ying Li, Anli Wei, Zhihong Liu   +3 more
doaj   +1 more source

On the covariance of the Moore-Penrose inverse

Linear Algebra and its Applications, 1983
AbstractIt is readily seen that the Moore-Penrose inverse A+ of a singular square matrix A does not for all regular matrices T satisfy the covariance condition (TAT−1)+ = TA+T−1. Thus the problem arises to describe the class C(A) of all those matrices T for which this condition is valid. The problem is solved for all matrices A of rank one and two.
openaire   +2 more sources

The Moore-Penrose inverse in rings with involution

Filomat, 2019
Let R be a unital ring with involution. In this paper, we first show that for an element a 2 R, a is Moore-Penrose invertible if and only if a is well-supported if and only if a is co-supported. Moreover, several new necessary and sufficient conditions for the existence of the Moore-Penrose inverse of an element in a ring R are obtained. In
Jianlong Chen, Sanzhang Xu
openaire   +4 more sources