Given multivariate data X1,,,,,,, XN (in Rp) in mean deviation form, let P be a p X p matrix, and define Yk = PT Xk for k = 1,,,,,,, N.
a. Show that Y1,,,,,,,,,,, YN are in mean-deviation form.
b. Show that if the covariance matrix of X1,,,,,,,,,, XN is S, then the covariance matrix of Y1,,,,,,,,, YN is PTSP.