Given multivariate data X1,...,XN (in R’) in mean- deviation form, let P be a pxp matrix, and define Y = P'Xx for k = 1, ., N. a. Show that Y1, ..., YN are in mean-deviation form. [Hint: Let w be the vector in RM with a 1 in each entry. Then [X| b. Show that if the covariance matrix of X1, ...,Xy is S, then the covariance matrix of Y1, ., YN is P™SP. XN ]w = 0 (the zero vector in RP).] ... ....
Given multivariate data X1,...,XN (in R’) in mean- deviation form, let P be a pxp matrix, and define Y = P'Xx for k = 1, ., N. a. Show that Y1, ..., YN are in mean-deviation form. [Hint: Let w be the vector in RM with a 1 in each entry. Then [X| b. Show that if the covariance matrix of X1, ...,Xy is S, then the covariance matrix of Y1, ., YN is P™SP. XN ]w = 0 (the zero vector in RP).] ... ....
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.6: Applications And The Perron-frobenius Theorem
Problem 70EQ
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