Let A E L(R). Suppose all solutions of x' = Ax are periodic with the same period. Then A is semisimple and the characteristic polynomial is a power of t² + a², a € R.
Let A E L(R). Suppose all solutions of x' = Ax are periodic with the same period. Then A is semisimple and the characteristic polynomial is a power of t² + a², a € R.
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.5: Iterative Methods For Computing Eigenvalues
Problem 46EQ
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