really, really simple

From: Stephen Miller (anon_at_hotmail.com)
Date: 06/22/04 

Date: Tue, 22 Jun 2004 16:56:07 +0000 (UTC)

Hi,

I have n-dimensional vectors x1, x2 and B

Now I reckon I know all the covariances of the coordinates, so I know

sigB (covariance matrix of B)

sigx1, sigx2

and even the cross terms ie. Cov[x1(i),B(j)], Cov[x1(i),x2(j)]

This is a bold claim and it isn't really true, however let's assume it
is. I want to know

Var(x1.B) and Cov(x1.B,x2.B)

I'm sure there is a simple matrix form, do you know it or know where I
can find it? (please don't sit there and work it out, I should be able
to do that myself)

Can anyone also verify, for my sanity, that in the case where
Cov[x1(i),B(j)]=0:

Var(x1.B)=x1^T*sigB*x1 + B^T*sigx1*B + Trace(sigB*sigx1) ?

Many thanks, my linear algebra is not what it once was!

Stephen

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