Hello,

I'm quite skeptical about your notations... What is "(covariance matrix)^(-1/2)" ? Is it the determinant of the covariance matrix ?

In this case, I don't see where

comes fromZ = (Covariance Matrix)^(-1/2) * (X_vector - mu_vector) N_p (0,I)

But Z^2 doesn't follow a normal distribution ??2) To say Z^2 does not mean (Covariance Matrix)^(-1/2) * (X_vector - mu_vector) * (Covariance Matrix)^(-1/2) * (X_vector - mu_vector). Instead the order changes to:

(X_vector - mu_vector)' * (Covariance Matrix)^(-1/2)*(Covariance Matrix)^(-1/2)* (X_vector - mu_vector).

Also, what is the square of a vector ?

It's rather "goes to N_p (0,I)" as n goes to infinity ?3) Finally trying to show sqrt(n) * (Covariance Matrix)^(-1/2) * (X_vector - mu_vector) is N_p (0,I).

But still, I don't agree with that formula...

It looks like the multidimensional central limit theorem. And unlike the unidimensional theorem, we cannot divide by the "standard deviation" (that you would have interpreted as (Covariance matrix)^(-1/2)) to get a "standard" normal distribution...

Where did you take these formulae from ?