## The Annals of Mathematical Statistics

### Bilinear Forms in Normally Correlated Variables

Allen T. Craig

#### Abstract

If a variable $x$ is normally distributed with mean zero, we have previously given a necessary and sufficient condition (see references at end of this paper) for the independence of two real symmetric quadratic forms in $n$ independent values of that variable. This condition is that the product of the matrices of the forms should vanish. In the present paper, we have proved that the same algebraic condition is both necessary and sufficient for the independence of two real symmetric bilinear, or a real symmetric bilinear and quadratic form, in normally correlated variables.

#### Article information

Source
Ann. Math. Statist., Volume 18, Number 4 (1947), 565-573.

Dates
First available in Project Euclid: 28 April 2007

https://projecteuclid.org/euclid.aoms/1177730347

Digital Object Identifier
doi:10.1214/aoms/1177730347

Mathematical Reviews number (MathSciNet)
MR23024

Zentralblatt MATH identifier
0029.30801

JSTOR