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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 com- ponents 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.]

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