Hotelling Deflation Assume that the largest eigenvalue ai in magnitude and an associated
Chapter 9, Problem 23(choose chapter or problem)
Hotelling Deflation Assume that the largest eigenvalue ai in magnitude and an associated eigenvector v (l) have been obtained for the n x n symmetric matrix A. Show that the matrix R - A - -v (1)tv(l) y (v"1 )'v"1 * ' hasthe same eigenvalues X2,... , as A, exceptthat B has eigenvalue 0 with eigenvector v < l) instead of eigenvector A|. Use this deflation method to find X2 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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