On a Schur complement inequality for the Hadamard product of certain totally nonnegative matrices.
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.
In this paper, we shall deal with the solvability of interval systems of linear equations in max-plus algebra. Max-plus algebra is an algebraic structure in which classical addition and multiplication are replaced by and , where , . The notation represents an interval system of linear equations, where and are given interval matrix and interval vector, respectively. We can define several types of solvability of interval systems. In this paper, we define the T4 solvability and give an algorithm...
We show that if a real non-singular matrix () has all its minors of order non-negative and has all its minors of order which come from consecutive rows non-negative, then all th order minors are non-negative, which may be considered an extension of Fekete’s lemma.
This paper gives a generalization of results presented by ten Berge, Krijnen,Wansbeek & Shapiro. They examined procedures and results as proposed by Anderson & Rubin, McDonald, Green and Krijnen, Wansbeek & ten Berge.We shall consider the same matter, under weaker rank assumptions. We allow some moments, namely the variance Ω of the observable scores vector and that of the unique factors, Ψ, to be singular. We require T' Ψ T > 0, where T Λ T' is a Schur decomposition of Ω. As...
Consider a non-centered matrix with a separable variance profile: Matrices and are non-negative deterministic diagonal, while matrix is deterministic, and is a random matrix with complex independent and identically distributed random variables, each with mean zero and variance one. Denote by the resolvent associated to , i.e. Given two sequences of deterministic vectors and with bounded Euclidean norms, we study the limiting behavior of the random bilinear form: as the dimensions...
The sign pattern of a real matrix , denoted by , is the -matrix obtained from by replacing each entry by its sign. Let denote the set of all real matrices such that . For a square real matrix , the Drazin inverse of is the unique real matrix such that , and , where is the Drazin index of . We say that has signed Drazin inverse if for any , where denotes the Drazin inverse of . In this paper, we give necessary conditions for some block triangular matrices to have signed...