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December, 1947 Bilinear Forms in Normally Correlated Variables
Allen T. Craig
Ann. Math. Statist. 18(4): 565-573 (December, 1947). DOI: 10.1214/aoms/1177730347

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.

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Allen T. Craig. "Bilinear Forms in Normally Correlated Variables." Ann. Math. Statist. 18 (4) 565 - 573, December, 1947. https://doi.org/10.1214/aoms/1177730347

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Published: December, 1947
First available in Project Euclid: 28 April 2007

zbMATH: 0029.30801
MathSciNet: MR23024
Digital Object Identifier: 10.1214/aoms/1177730347

Rights: Copyright © 1947 Institute of Mathematical Statistics

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Vol.18 • No. 4 • December, 1947
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