Given multivariate data X 1 ,..., X N (in R P ) in mean- deviation form, let

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Given multivariate data X1,..., X(in RP) in mean- deviation form, let P be a p x p matrix, and define Y= PT Xfor k = 1,..., N. 

a. Show that Y1,..., YN are in mean-deviation form. Let w be the vector in RN with a 1 in each entry. Then [X.......... XN]w = 0 (the zero vector in RP.

b. Show that if the covariance matrix of X1,..., XN is S, then the covariance matrix of Y1,..., Yis PTSP.

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Linear Algebra And Its Applications

ISBN: 9781292351216

6th Global Edition

Authors: David Lay, Steven Lay, Judi McDonald

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