Help on properties of symmetric matrices

Hi,

I'm reading a financial paper and my mind's drawing a blank on this following issue. Could you try help (please apologize my notation, I'm a Latex first-timer):

Say, where is a *nxn* real, symmetric variance-covariance matrix and is a *nxm* matrix

Let, and be the eigenvalues and respective eigenvectors and

where is a *nxm* orthogonal matrix comprising of those eigenvectors and is a *mxm* diagonal matrix comprising of the corresponding eigenvalues

I'll denote each element of matrix by

Let be a *mx1* vector of orthogonal processes

Then, prove that

Thanks,