Consider a multivariate t-distribution for which where A is an unknown positive definite matrix. Does this distribution function belong to the elliptically symmetric family ? Use the Courant Theorem...

Consider a multivariate t-distribution for which

where A is an unknown positive definite matrix. Does this distribution function belong to the elliptically symmetric family ? Use the Courant Theorem (on the ratio of two quadratic forms) to show that

for all x ∈ Rp. Hence, or otherwise, show that for 0 <>