Results 1 to 10 of about 66,143 (43)
The $m$-weak core inverse [PDF]
arXiv, 2023 Since the day the core inverse has been known in a paper of Bakasarly and Trenkler, it has been widely researched. So far, there are four generalizations of this inverse for the case of matrices of an arbitrary index, namely, the BT inverse, the DMP inverse, the core-EP inverse and the WC inverse.
arxiv
The generalized inverses of the quaternion tensor via the T-product [PDF]
arXiv, 2022 In this article, specific definitions of the Moore-Penrose inverse, Drazin inverse of the quaternion tensor and the inverse along two quaternion tensors are introduced under the T-product. Some characterizations, representations and properties of the defined inverses are investigated. Moreover, algorithms are established for computing the Moore-Penrose
arxiv
Finite and semisimple Boolean inverse monoids [PDF]
arXiv, 2021 We describe the structure of finite Boolean inverse monoids and apply our results to the representation theory of finite inverse semigroups. We then generalize to semisimple Boolean inverse semigroups.
arxiv
Further properties and representations of the W-weighted m-weak group inverse [PDF]
arXiv, 2023 The purpose of this paper is to explore more properties and representations of the W-weighted m-weak group (in short, W-m-WG) inverse. We first explore an interesting relation between two projectors with respect to the W-m-WG inverse. Then, the W-m-WG inverse is represented by various generalized inverses including W-weighted Drazin inverse, W-weighted
arxiv
A new class of generalized inverses in semigroups and rings with involution [PDF]
arXiv, 2022 Let $S$ be a $*$-semigroup and let $a,w,v\in S$. The initial goal of this work is to introduce two new classes of generalized inverses, called the $w$-core inverse and the dual $v$-core inverse in $S$. An element $a\in S$ is $w$-core invertible if there exists some $x\in S$ such that $awx^2=x$, $xawa=a$ and $(awx)^*=awx$.
arxiv
The generalized inverses of tensors via the C-Product [PDF]
arXiv, 2022 This paper studies the issues about the generalized inverses of tensors under the C-Product. The aim of this paper is threefold. Firstly, this paper present the definition of the Moore-Penrose inverse, Drazin inverse of tensors under the C-Product. Moreover, the inverse along a tensor is also introduced.
arxiv
On generalized inverses and Green's relations [PDF]
arXiv, 2009 We study generalized inverses on semigroups by means of Green's relations. We first define the notion of inverse along an element and study its properties. Then we show that the classical generalized inverses (group inverse, Drazin inverse and Moore-Penrose inverse) belong to this class.
arxiv
G-Drazin inverse combined with inner inverse [PDF]
This paper introduces new classes of generalized inverses for square matrices named GD1, and the dual, called 1GD inverse. In addition, we discuss a few characterizations and representations of these inverses. The explicit expressions of these inverses have been established via core-nilpotent decomposition.
arxiv +1 more source
Weighted weak group inverse for Hilbert space operators [PDF]
arXiv, 2019 We present the weighted weak group inverse, which is a new generalized inverse of operators between two Hilbert spaces, introduced to extend weak group inverse for square matrices. Some characterizations and representations of the weighted weak group inverse are investigated.
arxiv
Closed inverse subsemigroups of graph inverse semigroups [PDF]
arXiv, 2016 As part of his study of representations of the polycylic monoids, M.V. Lawson described all the closed inverse submonoids of a polycyclic monoid $P_n$ and classified them up to conjugacy. We show that Lawson's description can be extended to closed inverse subsemigroups of graph inverse semigroups. We then apply B.
arxiv