Related papers: Inverse M-matrix, a new characterization
This brief note concerns the invertibility of certain alternant matrices. In particular those that consisting of polynomials and products of polynomials and logarithms are shown to be invertible under appropriate conditions on the degrees…
We describe all inequalities among generalized diagonals in positive semi-definite matrices. These turn out to be governed by a simple partial order on the symmetric group. This provides an analogue of results of Drake, Gerrish, and…
Utilizing the notion of positive multilinear mappings, we give some matrix inequalities. In particular, Choi--Davis--Jensen and Kantorovich type inequalities including positive multilinear mappings are presented.
In this paper we introduce the generalized inverse of complex square matrix with respect to other matrix having same size. Some of its representations, properties and characterizations are obtained. Also some new representation matrices of…
Finite dimensional matrices having more columns than rows have no left inverses while those having more rows than columns have no right inverses. We give generalizations of these simple facts to bi--infinite matrices and use those to obtain…
To better understand the algebra $\mathcal{M}_n$ of all $n\times n$ complex matrices, we explore the class of accretive matrices. This class has received renowned attention in recent years due to its role in complementing those results…
The analysis of diagonalizable matrices in terms of their so-called isospectral reduction represents a versatile approach to the underlying eigenvalue problem. Starting from a symmetry of the isospectral reduction, we show in the present…
This paper examines the properties of real symmetric square matrices with a constant value for the main diagonal elements and another constant value for all off-diagonal elements. This matrix form is a simple subclass of circulant matrices,…
A transversal matroid whose dual is also transversal is called bi-transversal. Let $G$ be an undirected graph with vertex set $V$. In this paper, for every subset $W$ of $V$, we associate a bi-transversal matroid to the pair $(G,W)$. We…
We introduce a new type of reduction of inversive difference polynomials that is associated with a partition of the basic set of automorphisms $\sigma$ and uses a generalization of the concept of effective order of a difference polynomial.…
During routine state space circuit analysis of an arbitrarily connected set of nodes representing a lossless LC network, a matrix was formed that was observed to implicitly capture connectivity of the nodes in a graph similar to the…
In order to precondition Toeplitz systems, we present a new class of simultaneously diagonalizable real matrices, the Gamma-matrices, which include both symmetric circulant matrices and a subclass of the set of all reverse circulant…
The purpose of this paper is to analyze the Moore-Penrose pseudo-inversion of symmetric real matrices with application in the graph theory. We introduce a novel concept of positively and negatively pseudo-inverse matrices and graphs. We…
In this study, we give the dual characterizations of Mannheim offsets of the ruled surface in terms of their integral invariants and the new characterization of the Mannheim offsets of developable surface. Furthermore, we obtain the…
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…
In this paper, we systematically define and characterize various classes of Bohemian matrices with respect to the population $\mathbb{P}=\{0, \pm 1\}$, focusing on their inner and outer Bohemian inverses. The classes under consideration…
Inverse semigroups are a class of semigroups whose structure induces a compatible partial order. This partial order is examined so as to establish mirror properties between an inverse semigroup and the semilattice of its idempotent…
We introduce meta-factorization, a theory that describes matrix decompositions as solutions of linear matrix equations: the projector and the reconstruction equation. Meta-factorization reconstructs known factorizations, reveals their…
Decision analysis deals with modeling and enhancing decision processes. A principal challenge in improving behavior is in obtaining a transparent description of existing behavior in the first place. In this paper, we develop an expressive,…
We investigate the Moore-Penrose pseudoinverse and generalized inverse of a matrix product $A=CR$ to establish a unifying framework for generalized and randomized matrix inverses. This analysis is rooted in first principles, focusing on the…