Under the set up of Theorem 8 42, explain why Theorem 8 42 immediately implies that q j is a unit eigenvector of K associated with its j th largest eigenvalue j 2 j , which therefore is, up to a factor, the j th principal variance Summarizing, we have proved the Fundamental Theorem of Principal Com...

Theorem 842 provides the Singular Value Decomposition SVD of a data matrix X where X is an n p matri ...

Under the set-up of Theorem 8.42, explain why Theorem 8.42 immediately implies that q j is a

Question:

Under the set-up of Theorem 8.42, explain why

Theorem 8.42 immediately implies that q_jis a unit eigenvector of K associated with its j^th largest eigenvalue λ_j = σ²_j, which therefore is, up to a factor, the j^th principal variance. Summarizing, we have proved the Fundamental Theorem of Principal Component Analysis.