This is how we could understand the representation. Since we are ignorant on X, we use its swept form and set \mu_1 (\Sigma_{11})^{-1} = 0 and - (\Sigma_{11})^{-1} = 0. Since the correlation between X and Y is less than 1, the regression coefficient of X on Y approaches to 0 when the variance of X approaches to ∞. Therefore, (\Sigma_{11})^{-1} \Sigma_{12} = 0. Similarly, one can prove that \mu_1 (\Sigma_{11})^{-1} \Sigma_{12} = 0 and \Sigma_{21} (\Sigma_{11})^{-1} \Sigma_{12} = 0.
