Results 11 to 20 of about 66,143 (43)

P-canonical forms and complete inverses [PDF]

arXiv, 2020
This paper describes a new kind of inverse for elements in associative ring, that is the complete inverse, as the unique solution of a certain set of equations. This inverse exists for an element $a$ if and only if the Drazin inverse of $a$ exists. We also show that by plugging in $-k$ for $k$ in the $\mathcal{P}$-canonical form of a square matrix $A$,
arxiv  

Morita equivalence of inverse semigroups [PDF]

arXiv, 2011
We describe how to construct all inverse semigroups Morita equivalent to a given inverse semigroup. This is done by taking the maximum inverse images of the regular Rees matrix semigroups over the inverse semigroup where the sandwich matrix satisfies what we call the McAlister conditions.
arxiv  

Right core inverse and the related generalized inverses [PDF]

arXiv, 2018
In this paper, we introduce the notion of a (generalized) right core inverse and give its characterizations and expressions. Then, we provide the relation schema of (one-sided) core inverses, (one-sided) pseudo core inverses and EP elements.
arxiv  

Reverse order law for the inverse along an element [PDF]

arXiv, 2015
In this paper, we introduce a new concept called left (right) g-MP inverse in a $*$-monoid. The relations of this type of generalized inverse with left inverse along an element are investigated. Also, the reverse order law for the inverse along an element is studied.
arxiv  

Generalized core inverses of matrices [PDF]

arXiv, 2017
In this paper, we introduce two new generalized inverses of matrices, namely, the $\bra{i}{m}$-core inverse and the $\pare{j}{m}$-core inverse. The $\bra{i}{m}$-core inverse of a complex matrix extends the notions of the core inverse defined by Baksalary and Trenkler \cite{BT} and the core-EP inverse defined by Manjunatha Prasad and Mohana \cite{MM ...
arxiv  

Inverse Sets and Inverse Correspondences Over Inverse Semigroups [PDF]

arXiv
In this paper, we introduce notions called inverse set and inverse correspondence over inverse semigroups. These are analogies of Hilbert $C^*$-modules and \Ccorrs in the $C^*$-algebra theory. We show that inverse semigroups and inverse correspondences form a bicategory.
arxiv  

Inverse of the Gomory Corner Relaxation of Integer Programs [PDF]

arXiv
We analyze the inverse of the Gomory corner relaxation (GCR) of a pure integer program (IP). We prove the inverse GCR is equivalent to the inverse of a shortest path problem, yielding a polyhedral representation of the GCR inverse-feasible region. We present a linear programming (LP) formulation for solving the inverse GCR under the $L_{1}$ and $L_ ...
arxiv  

Inverse Privacy [PDF]

arXiv, 2015
An item of your personal information is inversely private if some party has access to it but you do not. We analyze the provenance of inversely private information and its rise to dominance over other kinds of personal information. In a nutshell, the inverse privacy problem is unjustified inaccessibility to you of your inversely private information. We
arxiv  

On inverse ordered semigroups [PDF]

arXiv, 2019
The purpose of this paper is to study the generalization of inverse semigroups (without order). An ordered semigroup S is called an inverse ordered semigroup if for every a 2 S, any two inverses of a are H-related. We prove that an ordered semigroup is complete semilattice of t-simple ordered semigroups if and only if it is completely regular and ...
arxiv  

Dagger-Drazin Inverses [PDF]

arXiv
Drazin inverses are a special kind of generalized inverses that can be defined for endomorphisms in any category. A natural question to ask is whether one can somehow extend the notion of Drazin inverse to arbitrary maps -- not simply endomorphisms. It turns out that this is possible and, indeed, natural to do so for dagger categories. This paper, thus,
arxiv