Related papers: Some notes about matrices, 4
We review some convexity inequalities for Hermitian matrices an add one more to the list.
We compute the degree complexity of the family of birational maps considered in \cite{bedford-kim-tuyen-abarenkova-maillard} for all exceptional cases. Some interesting properties of the family are also given.
In this paper, we consider several special polynomials related to associated sequences of polynomials. Finally, we give some new and interesting identities of those polynomials arising from transfer formula for the associated sequences.
We introduce an algorithm for computing closure systems derived from a family of implications on a set. Semilattices presentations are explored and used in conjunction with the algorithm to compute various types of lattices freely generated…
Brief review of concepts and unsolved problems in the theory of matrix models.
The different notions of matings of pairs of equal degree polynomials are introduced and are related to each other as well as known results on matings. The possible obstructions to matings are identified and related. Moreover the relations…
The aim of this note is to describe a geometric relation between simple plane curve singularities classified by simply laced Cartan matrices and cluster varieties of finite type also classified by the simply laced Cartan matrices. We…
In this paper we focus on two new families of polynomials which are connected with exponential polynomials and geometric polynomials. We discuss their generalizations and show that these new families of polynomials and their generalizations…
These notes deal with a few properties of convolutions in the role of approximations to the identity.
The paper explores the concept of the rank of a bicomplex matrix, delving into four distinct types of ranks and investigating conditions under which these ranks are equivalent. It also defines and analyzes the concept of idempotent row…
We define homological matrices, construct examples of one-dimension restricted homological quantum field theories, and show a relationship between the two theories.
Differential-difference integrable exponential type systems are studied corresponding to the Cartan matrices of semi-simple or affine Lie algebras. For the systems corresponding to the algebras $A_2$, $B_2$, $C_2$, $G_2$ the complete sets…
We study an elementary inequality supporting the classical Hermite-Hadamard inequality in the matrix setting. This leads to a number of interesting matrix inequalities such new Schatten p-norm estimates and new majorization
This note discusses an interesting matrix factorization called the CUR Decomposition. We illustrate various viewpoints of this method by comparing and contrasting them in different situations. Additionally, we offer a new characterization…
V. I. Arnold [Russian Math. Surveys 26, no. 2, 1971, 29-43] constructed smooth generic families of matrices with respect to similarity transformations depending smoothly on the entries of matrices and got bifurcation diagrams of such…
This paper is concerned with the taxonomy of finitely complete categories, based on 'matrix properties' - these are a particular type of exactness properties that can be represented by integer matrices. In particular, the main result of the…
We review principal results on axiomatizability of classes of lattices of equivalences
We derive formulae for Gram matrices arising in the Nyman--Beurling reformulation of the Riemann hypothesis. The development naturally leads upon series of the form $S(x) = \sum_{n\ge 1} R(nx)$ and their reciprocity relations. We give…
In this paper, certain mixed special polynomial families associated with Appell sequences are introduced and their properties are established. Further, operational rules providing connections between these families and the known special…
In recent years, random matrices have come to play a major role in computational mathematics, but most of the classical areas of random matrix theory remain the province of experts. Over the last decade, with the advent of matrix…