(Nondiagonal Jordan form) Consider a linear system with a Jordan form that is non-diagonal. (a) Prove Proposition 6.3 by showing that if the system contains a real eigenvalue 入 = O with a nontrivial Jordan block, then there exists an initial condition with a solution that grows in time. (b) Extend this argument to the case of complex eigenvalues with Reλ = 0 by using the block Jordan form Ji = 0 W 0 0 3000 1 0 0 1 0 ω 31 0

(Nondiagonal Jordan form) Consider a linear system with a Jordan form that is non-diagonal. (a) Prove Proposition 6.3 by showing that if the system contains a real eigenvalue 入 = O with a nontrivial Jordan block, then there exists an initial condition with a solution that grows in time. (b) Extend this argument to the case of complex eigenvalues with Reλ = 0 by using the block Jordan form Ji = 0 W 0 0 3000 1 0 0 1 0 ω 31 0

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter7: Distance And Approximation

Section7.4: The Singular Value Decomposition

Problem 26EQ

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