Related papers: Norms on complex matrices induced by complete homo…
We investigate the relationship between partial traces and their dilations for general complex matrices, focusing on two main aspects: the existence of (joint) dilations and norm inequalities relating partial traces and their dilations.…
The class of norm-dependent Random Matrix Ensembles is studied in the presence of an external field. The probability density in those ensembles depends on the trace of the squared random matrices, but is otherwise arbitrary. An exact…
We explore a natural extension of braid arrangements in the context of determinantal arrangements. We show that these determinantal arrangements are free divisors. Additionally, we prove that free determinantal arrangements defined by the…
A generic method for combinatorial constructions of intrinsic geometrical spaces is presented. It is based on the well known inverse sequences of finite graphs that determine (in the limit) topological spaces. If a pattern of the…
Properties of graphs that can be characterized by the spectrum of the adjacency matrix of the graph have been studied systematically recently. Motivated by the complexity of these properties, we show that there are such properties for which…
In this paper a general theory of semi-classical matrix orthogonal polynomials is developed. We define the semi-classical linear functionals by means of a distributional equation $D(u A) = u B,$ where $A$ and $B$ are matrix polynomials.…
This article aims at finding sufficient conditions for a family of meromorphic functions to be normal by involving partial sharing of sets with differential polynomials. Moreover, corresponding results for normal meromorphic functions are…
We study a new kind of symmetric polynomials P_n(x_1,...,x_m) of degree n in m real variables, which have arisen in the theory of numerical semigroups. We establish their basic properties and find their representation through the power sums…
We define tensors, corresponding to cubic polynomials, which have the same exponent $\omega$ as the matrix multiplication tensor. In particular, we study the symmetrized matrix multiplication tensor $sM_n$ defined on an $n\times n$ matrix…
We construct new families of completely regular codes by concatenation methods. By combining parity check matrices of cyclic Hamming codes, we obtain families of completely regular codes. In all cases, we compute the intersection array of…
In this paper we prove two new abstract compactness criteria in normed spaces. To this end we first introduce the notion of an equinormed set using a suitable family of semi-norms on the given normed space satisfying some natural…
This article presents an overview of the theory of integrable systems with symmetries, focusing on toric systems, semitoric systems, and their classifications via decorated polygons. We discuss certain one-parameter families of integrable…
Asymmetric vector norms are generalizations of asymmetric norms, where the subadditivity inequality is understood in ordered vector space sense. This relation imposes strong conditions on the ordering itself. This note studies on these…
This paper derives exponential tail bounds and polynomial moment inequalities for the spectral norm deviation of a random matrix from its mean value. The argument depends on a matrix extension of Stein's method of exchangeable pairs for…
We study geometric properties of trace functionals that generalize those in [Zhang, Adv. Math. 365:107053 (2020)], arising from a novel family of conditional entropies with applications in quantum information. Building on new convexity…
We introduce a new type of norm for ordered vector spaces majorized by a proper (convex) cone that generalizes the notions of order unit norm and base norm. Then we give sufficient conditions to ensure its completeness. In the case of…
We consider the set of $n\times n$ matrices with rational entries having numerator and denominator of size at most $H$ and obtain upper and lower bounds on the number of such matrices of a given rank and then apply them to count such…
Several recently discovered properties of multiple families of special polynomials (some orthogonal and some not) that satisfy certain differential, difference or q-difference equations are reviewed. A general method of construction of…
Permutation rational functions over finite fields have attracted high interest in recent years. However, only a few of them have been exhibited. This article studies a class of permutation rational functions constructed using trace maps on…
In this text we study the regularity of matrices with special polynomial entries. Barring some mild conditions we show that these matrices are regular if a natural limit size is not exceeded. The proof draws connections to generalized…