Eaton, Morris L. - In: Journal of Multivariate Analysis 6 (1976) 3, pp. 422-425
Let [Sigma] be an n - n positive definite matrix with eigenvalues [lambda]1 = [lambda]2 = ... = [lambda]n 0 and let M = {x, y x [epsilon] Rn, y [epsilon] Rn, x [not equal to] 0, y [not equal to] 0, x'y = 0}. Then for x, y in M, we have that x'[Sigma]y/(x'[Sigma]xy'[Sigma]y)1/2 = ([lambda]1 -...
