Related papers: Weak group inverse
The W-set of an element of a weak order poset is useful in the cohomological study of the closures of spherical subgroups in generalized flag varieties. We explicitly describe in a purely combinatorial manner the W-sets of the weak order…
We analyze two weak random operators, initially motivated from processes in random environment. Intuitively speaking these operators are ill-defined, but using bilinear forms one can deal with them in a rigorous way. This point of view can…
In this paper, we introduce the concept of the m-generalized right group inverse. This serves as a natural extension of both the m-weak group inverse and the generalized group inverse. We characterize this new generalized inverse using the…
We present the existence of the group inverse and its representation for the block operator matrix $\left( \begin{array}{cc} E&I\\ F&0 \end{array} \right)$ under the condition $FEF^{\pi}=0$. The group inverse for the anti-triangular block…
The aim of this paper is to generalize the Core Inverse to arbitrary vector spaces using finite potent endomorphisms. As an application, the core partial order is studied in the set of finite potent endomorphisms (of index lesser or equal…
We study generalized inverses for matrices associated with double star digraphs. Explicit block formulas and existence criteria are obtained for core, dual core, core EP, and dual core EP inverses, expressed in terms of explicit algebraic…
We describe the additive subgroups of fields which are closed with respect to taking inverses. In particular, in characteristic different from two any such subgroup is either a subfield or the kernel of the trace map of a quadratic…
In this paper, we introduce the m-core-EP inverse in Minkowski space, consider its properties, and get several sufficient and necessary conditions for the existence of the m-core-EP inverse. We give the m-core-EP decomposition in Minkowski…
For an $n$-tuple $s$ of non-negative integers, the $s$-weak order is a lattice structure on $s$-trees, generalizing the weak order on permutations. We first describe the join irreducible elements, the canonical join representations, and the…
In this article we present a new characterization of inverse M-matrices, inverse row diagonally dominant M-matrices and inverse row and column diagonally dominant M-matrices, based on the positivity of certain inner products.
In this paper, we introduce the classes of weakly surjunctive and linearly surjunctive groups which include all sofic groups and more generally all surjunctive groups. We investigate various properties of such groups and establish in…
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…
Algorithmic methods for the explicit inversion of the indefinite double covering maps are proposed. These are based on either the Givens decomposition or the polar decomposition of the given matrix in the proper, indefinite orthogonal group…
It is known that an inverse monoid $M$ is E-unitary if and only if the following diagram is an extension: $E(M) \to M \to M/\sigma$, where $E(M)$ is the semilattice of idempotents and $M/\sigma$ is the minimal group quotient. F-inverse…
An element $g$ of a group is called {\em reversible} if it is conjugate in the group to its inverse. This paper is about reversibles in the group $G$ of formally-invertible pairs of formal power series in two variables, with complex…
We present new properties of generalized core-EP inverse in a Banach *-algebra. We characterize this new generalized inverse by using involved annihilators. The generalized core-EP inverse for products is obtained. The core-EP orders for…
In this paper, we provide a few properties of the weighted Moore--Penrose inverse for an arbitrary order tensor via the Einstein product. We again obtain some new sufficient conditions for the reverse-order law of the weighted…
We study the partial orders induced on Wachs and signed Wachs permutations by the Bruhat and weak orders of the symmetric and hyperoctahedral groups. We show that these orders are graded, determine their rank function, characterize their…
This manuscript proposes a generalized inverse for a dual matrix called dual Drazin generalized inverse (DDGI) which generalizes the notion of the dual group generalized inverse (DGGI). Under certain necessary and sufficient conditions, we…
In this article, we propose to initiate the general study of involution systems. An {\em involution system}, that is, a group $W$ generated by a set of involutions $S$, is naturally endowed with a {\em weak order} arising from orienting the…