Quote:

Third : Sorry, I mistyped! Should be:

3) Finally trying to show sqrt(n) * (Covariance Matrix)^(-1/2) * (SampleMean_vector - mu_vector) is N_p (0,I).

Applied Multivariate Statistical Analysis by Johnson and Wichern

Are you able to help?

The sample mean vector is (let's call it Z) $\displaystyle Z=\frac 1n \sum_{i=1}^n X_i$. Quote:

Second: The book shows shows Z^2 =

(X_vector - mu_vector)' * (Covariance Matrix)^(-1/2)*(Covariance Matrix)^(-1/2)* (X_vector - mu_vector). And then notes it is distributed chi-square.

where Z is (Covariance Matrix)^(-1/2) * (X_vector - mu_vector) N_p (0,I)

My question is how do you know the order to set up the multiplication to get Z^2?

Same problem here. Need to think on that later on...