How Can the Variance of a Quadratic Form Be Simplified?

[zli034]

In the Searle's 1971 book Linear Model, page 57, has a formula for the Variance of Quadratic form:

var(Y^{T}AY)=2tr(A\SigmaA\Sigma)+4\mu^{T}A\SigmaA\mu

The proof of this showed on page 55 was based on MGF. I'm looking for proofs are less complicated. Some thing that is similar to show the expectation of a quadratic form.

Anyone has read about quadratic form please help.

Thanks

 

[bpet]

If you're talking about a constant matrix A and a random vector Y that is jointly gaussian, one way is to write the quadratic form as a double sum.