Notes on the divisibility of GCD and LCM matrices.
Number variance from a probabilistic perspective: infinite systems of independent Brownian motions and symmetric -stable processes.
Numerical Solution of Linear Equations with Toeplitz and Vector Toeplitz Matrices.
On a bound on algebraic connectivity: the case of equality
In a recent paper the authors proposed a lower bound on , where , , is an eigenvalue of a transition matrix of an ergodic Markov chain. The bound, which involved the group inverse of , was derived from a more general bound, due to Bauer, Deutsch, and Stoer, on the eigenvalues of a stochastic matrix other than its constant row sum. Here we adapt the bound to give a lower bound on the algebraic connectivity of an undirected graph, but principally consider the case of equality in the bound when...
On a cell decomposition for Hankel matrices and rational functions.
On a class of linear models.
This paper is concerned with classification criteria, asymptotic behaviour and stationarity of a non-Markovian model with linear transition rule, called a linear OM-chain. This problems are solved by making use of the structure of the stochastic matrix appearing in the definition of such a model. The model studied includes as special cases the Markovian model as well as the linear learning model, and has applications in psychological and biological research, in control theory, and in adaptation...
On a class of matrices which arise in the numerical solution of Euler equations.
On a classic example in the nonnegative inverse eigenvalue problem.
On a Companion Operator for Analytic Functions.
On a decomposition of square matrices over a ring with identity.
On a direct method for the solution of nearly uncoupled Markov chains.
On a generalization of the Van Der Waerden conjecture
On a geometric property of positive definite matrices cone.
On a -polar decomposition of a bounded operator and matrices of -symmetric and -skew-symmetric operators.
On a nonnegative irreducible matrix that is similar to a positive matrix
Let A be an n×n irreducible nonnegative (elementwise) matrix. Borobia and Moro raised the following question: Suppose that every diagonal of A contains a positive entry. Is A similar to a positive matrix? We give an affirmative answer in the case n = 4.
On a Schur complement inequality for the Hadamard product of certain totally nonnegative matrices.
On a strong form of a conjecture of Boyle and Handelman.
On a surprising relation between the Marchenko–Pastur law, rectangular and square free convolutions
In this paper, we prove a result linking the square and the rectangular R-transforms, the consequence of which is a surprising relation between the square and rectangular versions the free additive convolutions, involving the Marchenko–Pastur law. Consequences on random matrices, on infinite divisibility and on the arithmetics of the square versions of the free additive and multiplicative convolutions are given.
On a theorem of Everitt, Thompson, and de Pillis
On an exposed element of a set of doubly stochastic rectangular matrices