Solved: Hotelling Deflation Assume that the largest eigenvalue 1 in magnitude and an
Chapter 9, Problem 17(choose chapter or problem)
Hotelling Deflation Assume that the largest eigenvalue 1 in magnitude and an associated eigenvector v(1) have been obtained for the n n symmetric matrix A. Show that the matrix B = A 1 (v(1))t v(1) v(1) (v(1) ) t has the same eigenvalues 2, ... , n as A, except that B has eigenvalue 0 with eigenvector v(1) instead of eigenvector 1. Use this deflation method to find 2 for each matrix in Exercise 5. Theoretically, this method can be continued to find more eigenvalues, but round-off error soon makes the effort worthless.
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