The inverse tangent law for the solutions of systems of linear algebraic equations with independent random coefficients is proven under Linderberg's condition.
type: Item
instance of: scholarly article
title: The inverse tangent law for the solutions of systems of linear algebraic equations with independent random coefficients is proven under Linderberg's condition.
zbMATH Open document ID: 1393.15005
author: Vyacheslav Girko
author: Larissa D. Shevchuk
published in: Random Operators and Stochastic Equations
publication date: 2018-06-06T00:00:00Z
review text: The system of linear algebraic equations \[ \Xi_{n\times n}\vec x_n=\vec \eta_n, \] where \(n=1,2,\dots ,\;\) \(\Xi_{n\times n}=\bigl[\xi_{ij}^{(n)}\bigr]_{i,j=1,\dots n}\), \(\vec \eta_n^{\top}=\{\eta_i^{(n)} : i=1,\dots,n\}\), \(\vec x_n^{\top}=\{x_i^{(n)} : i=1,\dots, n\}\) with independent random coefficients is considered. The inverse tangent law for such a system is proved under the Lindeberg's condition. The paper is a continuation and generalization of previous results of the first author, (see for example [Random Oper. Stoch. Equ. 19, No. 4, 299--312 (2011; Zbl 1268.60005)]).
Mathematics Subject Classification ID: 15A06
Mathematics Subject Classification ID: 15B52
zbMATH DE Number: 6881624
zbMATH Keywords: random matrix
zbMATH Keywords: eigenvalues
zbMATH Keywords: inverse tangent law
reviewed by: Michal Zajac
MaRDI profile type: Publication
full work available at URL: rose-2018-0010
OpenAlex ID: W2805266497
cites work: Q3930360
cites work: Q3999677
cites work: Q4331756
cites work: Q4246761
cites work: Q2778809
cites work: 35 years of the Inverse Tangent Law
cites work: DISTRIBUTION OF EIGENVALUES FOR SOME SETS OF RANDOM MATRICES
Wikidata QID: Q129757335
DOI: 10.1515/ROSE-2018-0010
description: scientific article; zbMATH DE number 6881624