On the Distribution of a Quadratic Form in Normal Variates

Abstract

It is a well-known theorem in linear models that the idempotency of a matrix is a sufficient and necessary condition for a quadratic form in normal variates to have a chisquare distribution, but its proofs in the early literature were incorrect or incomplete. Driscoll (1999) provided an improved proof, and this article presents a simple proof. More importantly, we establish and prove a generalized theorem.