Related papers: On generalized inverses of matrices associated wit…
We explore properties of generalized Paley graphs and we extend a result of Lim and Praeger by providing a more precise description of the connected components of disconnected generalized Paley graphs. This result leads to a new…
The {\it inversion} of a set $X$ of vertices in a digraph $D$ consists in reversing the direction of all arcs of $D\langle X\rangle$. The {\it inversion number} of an oriented graph $D$, denoted by ${\rm inv}(D)$, is the minimum number of…
We present the explicit inverse of a class of symmetric tridiagonal matrices which is almost Toeplitz, except that the first and last diagonal elements are different from the rest. This class of tridiagonal matrices are of special interest…
We prove that the (non-symmetric) adjacency matrix of a uniform random $d$-regular directed graph on $n$ vertices is asymptotically almost surely invertible, assuming $\min(d,n-d)\ge C\log^2n$ for a sufficiently large constant $C>0$. The…
In this paper we prove Morse index theorems for a big class of constrained variational problems on graphs. Such theorems are useful in various physical and geometric applications. Our formulas compute the difference of Morse indices of two…
A graphical model encodes conditional independence relations via the Markov properties. For an undirected graph these conditional independence relations can be represented by a simple polytope known as the graph associahedron, which can be…
We study divergence and thickness for general Coxeter groups $W$. We first characterise linear divergence, and show that if $W$ has superlinear divergence then its divergence is at least quadratic. We then formulate a computable…
Let $R$ be a ring with identity and $J(R)$ be its Jacobson radical. Assume that $a\in R$ is $(b,c)$-invertible and $j_a,j_b,j_c\in J(R)$. This paper provides necessary and sufficient conditions for $a+j_a$ to be $(b+j_b,c+j_c)$-invertible.…
In this paper, we introduce the notion of weak core and central weak core inverse in a {\it proper $*$-ring}. We further elaborate on these two classes by producing a few representations and characterizations of the weak core and central…
We study two classes of inverse semigroups built from directed graphs, namely graph inverse semigroups and a new class of semigroups that we refer to as Leavitt inverse semigroups. These semigroups are closely related to graph…
A generalization with singular weights of Moore-Penrose generalized inverses of closed range operators in Hilbert spaces is studied using the notion of compatibility of subspaces and positive operators.
We study property testing of (di)graph properties in bounded-degree graph models. The study of graph properties in bounded-degree models is one of the focal directions of research in property testing in the last 15 years. However, despite…
A matrix (and any associated linear system) will be referred to as structured if it has a small displacement rank. It is known that the inverse of a structured matrix is structured, which allows fast inversion (or solution), and reduced…
In this paper we discuss graph inverse semigroups which are constucted from a directed graphs and study several interesting properties of graph inverse semigroups such as the nature of its idempotents, the structure of semilattice of…
The purpose of this note is to give explicit criteria to determine whether a real generalized Cartan matrix is of finite type, affine type or of hyperbolic type by considering the principal minors and the inverse of the matrix. In…
In this paper we characterize Moore-Penrose inverses of Gram matrices leaving a cone invariant in an indefinite inner product space using indefinite matrix multiplication. This characterization includes the acuteness (or obtuseness) of…
In the last decades the Moore-Penrose pseudoinverse has found a wide range of applications in many areas of Science and became a useful tool for physicists dealing, for instance, with optimization problems, with data analysis, with the…
Toral automorphisms, represented by unimodular integer matrices, are investigated with respect to their symmetries and reversing symmetries. We characterize the symmetry groups of GL(n,Z) matrices with simple spectrum through their…
An oriented graph $D$ is converse invariant if, for any tournament $T$, the number of copies of $D$ in $T$ is equal to that of its converse $-D$. El Sahili and Ghazo Hanna [J. Graph Theory 102 (2023), 684-701] showed that any oriented graph…
Symplectic geometry plays an increasingly important role in mathematics, physics and applications, and naturally gives rise to interesting matrix families and properties. One of these is the notion of symplectic eigenvalues, whose existence…