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# The variances of the principal components are the same for Y and rotated Y

2017-09-08 06:30:05

I got this question on the textbook. How to solve this? Thank you.

Suppose Y is a data matrix, and Z = YF for some orthogonal matrix F, so that Z is a rotated version of Y. Show that the variances of the principal components are the same for Y and Z. (This result should make intuitive sense.) [Hint:

Find the spectral decomposition of the covariance of Z from that of Y, then note that these covariance matrices have the same eigenvalues.]