Related papers: Divisibility of LCM matrices by Totally nonnegativ…

Generalized parton distributions (GPDs) serve as indispensable tools for the exploration of proton structure. In this study, we offer a deep learning-assisted framework for the extraction of GPDs from experimental data and the results of…

Linear Complementary Pairs (LCP) of algebraic geometry (AG) codes offer strong resistance against side-channel and fault-injection attacks, but their construction depends critically on the explicit identification of non-special divisors of…

Given a finite set $\{M_0,\dots,M_{d-1}\}$ of nonnegative $2\times 2$ matrices and a nonnegative column-vector $V$, we associate to each $(\omega_n)\in\{0,\dots,d-1\}^\mathbb N$ the sequence of the column-vectors…

Variables of separation for classical $GL(3)$ magnetic chain obtained by Sklyanin form a generic positive divisor $D$ of degree $n$ on a genus $g$ non-hyperelliptic algebraic curve. Because $n>g$ this divisor $D$ has unique representative…

Commutators and anticommutators of gamma matrices with arbitrary numbers of (antisymmetrized) indices are derived.

This paper explicitly details the relation between $M$-matrices, nonnegative roots of nonnegative matrices, and the embedding problem for finite-state stationary Markov chains. The set of nonsingular nonnegative matrices with arbitrary…

For each $n \geq 1$ and sign pattern $\epsilon \in \{ \pm 1 \}^n$, we introduce a cone of real symmetric matrices $LPM_n(\epsilon)$: those with leading principal $k \times k$ minors of signs $\epsilon_k$. These cones are pairwise disjoint…

The algebra of ${\rm GL}_n$-invariants of $m$-tuples of $n\times n$ matrices with respect to the action by simultaneous conjugation is a classical topic in case of infinite base field. On the other hand, in case of a finite field generators…

The matrix semigroup membership problem asks, given square matrices $M,M_1,\ldots,M_k$ of the same dimension, whether $M$ lies in the semigroup generated by $M_1,\ldots,M_k$. It is classical that this problem is undecidable in general but…

Let $ R \subset \R $ be a GCD-domain. In this paper, Weinberg's conjecture on the $ n \times n $ matrix algebra $ M_{n}(R) \ (n \geq 2) $ is proved. Moreover, all the lattice orders (up to isomorphisms) on a full $ 2 \times 2 $ matrix…

In this paper we study zero--divisor graphs of rings and semirings. We show that all zero--divisor graphs of (possibly noncommutative) semirings are connected and have diameter less than or equal to 3. We characterize all acyclic…

We introduce a new technique for proving positivity of certain divisor classes on $\bar{M}_{0,n}$ and its weighted variants. Our methods give an unconditional description of the spaces of symmetric weighted pointed rational curves as log…

Let $K$ be a field and let $\sigma$ be an automorphism and let $\delta$ be a $\sigma$-derivation of $K$. Then we show that the multiplicative group of nonzero elements of the division ring $D=K(x;\sigma,\delta)$ contains a free non-cyclic…

Although a good portion of elementary linear algebra concerns itself with matrices over a field such as $\mathbb{R}$ or $\mathbb{C}$, many combinatorial problems naturally surface when we instead work with matrices over a finite field. As…

In this survey article, we describe recent work that connects three separate objects of interest: totally nonnegative matrices; quantum matrices; and matrix Poisson varieties.

A full determination of the CKM matrix using recent results from lattice QCD is presented. To extract the CKM matrix in a uniform fashion, I exclusively use results from unquenched lattice QCD as the theory input for nonperturbative QCD…

Using a new definition of generalized divisors we prove that the lattice of such divisors for a given linear partial differential operator is modular and obtain analogues of the well-known theorems of the Loewy-Ore theory of factorization…

In this paper we consider the decomposition of positive semidefinite matrices as a sum of rank one matrices. We introduce and investigate the properties of various measures of optimality of such decompositions. For some classes of positive…

This paper introduces a class of rings called left nil zero semicommutative rings ( LNZS rings ), wherein a ring R is said to be LNZS if the left annihilator of every nilpotent element of R is an ideal of R. It is observed that reduced…

In this note, we give a necessary and sufficient condition for a matrix A in M to be finitely G-determined, where M is the ring of 2 x 2 matrices whose entries are formal power series over an infinite field, and G is a group acting on M by…