A limit theorem for the eigenvalues of product of two random matrices
type: Item
instance of: scholarly article
title: A limit theorem for the eigenvalues of product of two random matrices
zbMATH Open document ID: 0553.62018
DOI: 10.1016/0047-259X(83)90035-0
author: Y. Q. Yin
author: P. R. Krishnaiah
published in: Journal of Multivariate Analysis
publication date: 1983-01-01T00:00:00Z
review text: If \(A_ p\) is a \(p\times p\) matrix with real eigenvalues, and \(pF_ p(x)\) is the number of eigenvalues less than or equal to x, then we call \(F_ p(x)\) the spectral distribution function of \(A_ p\). Let \(W_ p=X_ pX^ T_ p\) be a Wishart matrix where \(X_ p\) is \(p\times m\) dimensional. Let \(T_ p\) be a \(p\times p\) symmetric matrix of random variables. Under certain conditions the authors prove that if \(F_ p\) is the spectral distribution function of \(m^{-1}W_ pT_ p\), then there exists a distribution function F such that \(F_ p(x)\) converges in probability to \(F(x)\), for any x, as p increases without limit.
Mathematics Subject Classification ID: 62E20
Mathematics Subject Classification ID: 62H10
zbMATH DE Number: 3881667
zbMATH Keywords: product of two random matrices
zbMATH Keywords: real eigenvalues
zbMATH Keywords: spectral distribution function
zbMATH Keywords: Wishart matrix
zbMATH Keywords: symmetric matrix of random variables
reviewed by: Kenneth S. Miller
MaRDI profile type: Publication
cites work: Q5545069
cites work: Q5512461
cites work: Spectral Analysis of Networks with Random Topologies
cites work: Some limit theorems for the eigenvalues of a sample covariance matrix
cites work: The strong limits of random matrix spectra for sample matrices of independent elements
cites work: On the distribution of the roots of certain symmetric matrices
full work available at URL: 0047-259x(83)90035-0
OpenAlex ID: W3143198474
description: scientific article; zbMATH DE number 3881667