On Wielandt's Inequality and Its Application to the Asymptotic Distribution of the Eigenvalues of a Random Symmetric Matrix

Abstract

A relatively obscure eigenvalue due to Wielandt is used to give a simple derivation of the asymptotic distribution of the eigenvalues of a random symmetric matrix. The asymptotic distributions are obtained under a fairly general setting. An application of the general theory to the bootstrap distribution of the eigenvalues of the sample covariance matrix is given.