# Homework Help: Rotational invariance

1. Apr 23, 2010

### dymin3

suppose that X and Y are independent and each rotationally invariant on Rk

a) Let P denote any orthogonal projection with dim P = k1
determine the distribution of the correlation coefficient r= X'PY/(|PX||PY|)

I think r is a special case of ∑(Xi-barX)(Yi-barY) = X'PX where P = I-n^(-1)11'
but what should I do after?

b) Let X = X1 with Xi on Rki where i =1,2 and prove
X2
- Each Xi is rotationally invariant in its own right

I tried to prove Maxwell-Hershell [Maxwell-Hershell: x1,...,xn iid N(0,σ2) iff x is rotationally invariant and x1,..,xn are independent] but i was not sure...

- If Vi is in R[from K1 to K] with V'V = I, then V'X = X1

This one, I was not sure how to start T-T

Last edited: Apr 23, 2010