Related papers: Matrices with prescribed row and column sums

In this paper, we consider classes of decision tables with 0-1-decisions closed relative to removal of attributes (columns) and changing decisions assigned to rows. For tables from an arbitrary closed class, we study the dependence of the…

We define two notions of partial sums of a Riordan array, corresponding respectively to the partial sums of the rows and the partial sums of the columns of the Riordan array in question. We characterize the matrices that arise from these…

Brualdi and Ma found a connection between involutions of length $n$ with $k$ descents and symmetric $k\times k$ matrices with non-negative integer entries summing to $n$ and having no row or column of zeros. From their main theorem they…

A new family of asymmetric matrices of Walsh-Hadamard type is introduced. We study their properties and, in particular, compute their determinants and discuss their eigenvalues. The invertibility of these matrices implies that certain…

Relational data are often represented as a square matrix, the entries of which record the relationships between pairs of objects. Many statistical methods for the analysis of such data assume some degree of similarity or dependence between…

A set of independence statements may define the independence structure of interest in a family of joint probability distributions. This structure is often captured by a graph that consists of nodes representing the random variables and of…

In the course of studies of the measure of chaos for the distribution of the prime numbers among the positive integers N arched structures have been found. It is given a brief description of the fine structure of the positive integers…

Random matrices arise in many mathematical contexts, and it is natural to ask about the properties that such matrices satisfy. If we choose a matrix with integer entries at random, for example, what is the probability that it will have a…

The paper discusses progress in understanding statistical properties of complex eigenvalues (and corresponding eigenvectors) of weakly non-unitary and non-Hermitian random matrices. Ensembles of this type emerge in various physical…

We initiate a study of the zero-nonzero patterns of n by n alternating sign matrices. We characterize the row (column) sum vectors of these patterns and determine their minimum term rank. In the case of connected alternating sign matrices,…

In this paper we parameterize non-negative matrices of sum one and rank at most two. More precisely, we give a family of parameterizations using the least possible number of parameters. We also show how these parameterizations relate to a…

Let $n$ be a positive integer and $X = [x_{ij}]_{1 \leq i, j \leq n}$ be an $n \times n$\linebreak \noindent sized matrix of independent random variables having joint uniform distribution $$\hbox{Pr} {x_{ij} = k \hbox{for} 1 \leq k \leq n}…

Ensembles of random stochastic and bistochastic matrices are investigated. While all columns of a random stochastic matrix can be chosen independently, the rows and columns of a bistochastic matrix have to be correlated. We evaluate the…

We present a general methodology for performing statistical inference on the components of a real-valued matrix parameter for which rows and columns are subject to order restrictions. The proposed estimation procedure is based on an…

This is survey of some recent results connecting random matrices, non-colliding processes and queues.

We describe a framework for random pairwise comparisons matrices, inspired by selected constructions releted to the so called inconsistency reduction of pairwise comparisons (PC) matrices. In to build up structures on random pairwise…

We present correspondences induced by some classical mappings between measures on an interval and measures on the unit circle. More precisely, we link their sequences of orthogonal polynomial and their recursion coefficients. We also deduce…

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…

We define a set of binary matrices where any two of them can not be placed one on the other in a way such that the corresponding entries coincide. The rows of the matrices are obtained by means of Dyck words. The cardinality of the set of…

We discuss isoperimetric inequalities for convex sets. These include the classical isoperimetric inequality and that of Brunn-Minkowski, Blaschke-Santalo, Busemann-Petty and their various extensions. We show that many such inequalities…