Theorem proof:

where X1 and X2 are k x 1 and (n k) x 1 vectors respectively, and 11 and #12 are the expectation vectors of X1 and X2 respectively. Similarly, let 211 I312) 21 = , (212 222 where 211 is the k x k correlation matrix ole, 222 is the (n k) x (n k) correlation matrix ofXg, 212 is the corresponding (n k) x 1: matrix, and 221 is the corresponding k x (n k) matrix