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(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 eigenvalues A 22 of S. Show that %3D (i) ; = 0, j = 1, .9 (ii) s, = A,.j = 1,. q %3D

(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 eigenvalues A 22 of S. Show that %3D (i) ; = 0, j = 1, .9 (ii) s, = A,.j = 1,. q %3D

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter7: Eigenvalues And Eigenvectors
Section7.CR: Review Exercises
Problem 15CR: For what values of a does the matrix A=[01a1] have the characteristics below? a A has eigenvalue of...
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(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
Transcribed Image 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
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