(b) (For Math 5090 students) Let X be an nxq data matrix, S its sample covariance matrix and y, j = 1,.q. the principal components associated with eigenvahues A 2. of S. Show that (i) = 0, j = 1, . 9...

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Extracted text: (b) (For Math 5090 students) Let X be an nxq data matrix, S its sample covariance matrix and y, j = 1,.q. the principal components associated with eigenvahues A 2. of S. Show that (i) = 0, j = 1, . 9 (ii) s, = A,.j = 1, . q (iii) Cov(yi, y,) = 0, i # j (iv) E-1, = trace(S) (v) IT-1 , = |S|. %3D