## The Annals of Statistics

- Ann. Statist.
- Volume 19, Number 1 (1991), 260-271.

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

Morris L. Eaton and David E. Tyler

#### 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.

#### Article information

**Source**

Ann. Statist. Volume 19, Number 1 (1991), 260-271.

**Dates**

First available in Project Euclid: 12 April 2007

**Permanent link to this document**

http://projecteuclid.org/euclid.aos/1176347980

**Digital Object Identifier**

doi:10.1214/aos/1176347980

**Mathematical Reviews number (MathSciNet)**

MR1091849

**Zentralblatt MATH identifier**

0742.62015

**JSTOR**

links.jstor.org

**Subjects**

Primary: 62H25: Factor analysis and principal components; correspondence analysis

Secondary: 62E20: Asymptotic distribution theory

**Keywords**

Bootstrap covariance matrix eigenvalues random symmetric matrices

#### Citation

Eaton, Morris L.; Tyler, David E. On Wielandt's Inequality and Its Application to the Asymptotic Distribution of the Eigenvalues of a Random Symmetric Matrix. Ann. Statist. 19 (1991), no. 1, 260--271. doi:10.1214/aos/1176347980. http://projecteuclid.org/euclid.aos/1176347980.