(a) If the eigenvalues of the n x n matrix A are λ > λ > 13 ...λ = 0 show that the eigenvalue λ,, can be found by applying the power method to the matrix k/-A, where is the identity matrix and k> 2₁.

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter5: Orthogonality
Section5.4: Orthogonal Diagonalization Of Symmetric Matrices
Problem 16EQ
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1.5.3
(a) If the eigenvalues of the n x n matrix A are
λ > λ > 13... λ = 0
show that the eigenvalue λ, can be found by
applying the power method to the matrix kl - A,
where is the identity matrix and k > 2₁.
Transcribed Image Text:1.5.3 (a) If the eigenvalues of the n x n matrix A are λ > λ > 13... λ = 0 show that the eigenvalue λ, can be found by applying the power method to the matrix kl - A, where is the identity matrix and k > 2₁.
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