## The Annals of Mathematical Statistics

### The Distribution of the Latent Roots of the Covariance Matrix

Alan T. James

#### Abstract

The distribution of the latent roots of the covariance matrix calculated from a sample from a normal multivariate population, was found by Fisher [3], Hsu [6] and Roy [10] for the special, but important case when the population covariance matrix is a scalar matrix, $\Sigma = \sigma^2I$. By use of the representation theory of the linear group, we are able to obtain the general distribution for arbitrary $\Sigma$.

#### Article information

Source
Ann. Math. Statist., Volume 31, Number 1 (1960), 151-158.

Dates
First available in Project Euclid: 27 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aoms/1177705994

Digital Object Identifier
doi:10.1214/aoms/1177705994

Mathematical Reviews number (MathSciNet)
MR126901

Zentralblatt MATH identifier
0201.52401

JSTOR
links.jstor.org

#### Citation

James, Alan T. The Distribution of the Latent Roots of the Covariance Matrix. Ann. Math. Statist. 31 (1960), no. 1, 151--158. doi:10.1214/aoms/1177705994. https://projecteuclid.org/euclid.aoms/1177705994