If ldet(A)I > 1, prove that the powers An cannot stay bounded. But if ldet(A)I :S 1, show that some entries of An might still grow large. Eigenvalues will give the right test for stability, determinants tell us only one number.
If ldet(A)I > 1, prove that the powers An cannot stay bounded. But if ldet(A)I :S 1, show that some entries of An might still grow large. Eigenvalues will give the right test for stability, determinants tell us only one number.
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.2: Determinants
Problem 20EQ
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If ldet(A)I > 1, prove that the powers An cannot stay bounded. But if ldet(A)I :S 1, show that some entries of An might still grow large. Eigenvalues will give the right test for stability, determinants tell us only one number.
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