Following Theorem 6.6 prove that the reciprocal proportionality model (Section 6.4.1) is invariant with respect to scaling of the observed random variables.
THEOREM 6.6
Let X he a random vector with nonsingular covariance matrix Σ. Then the weighted covariance matrix Σ* = Ψ-1/2 Σ Ψ-1/2 is invariant under a scale transformation of X.