# The jordan form yields some explicit information

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Unformatted text preview: ion Theorem, is given by . If is an is nilpotent of order matrix of form [2] and is a real eigenvalue of then where and , …. Then . Similarly, if of , then is an matrix of form [3] and where is a complex eigenvalue 10 Chapter 2 part B is nilpotent of order and , where is the rotation matrix . This form of the solution to [3] leads to the following result. Corollary. Each coordinate in the solution combination of functions of form or where of the initial value problem [4] is a linear , is an eigenvalue of the matrix More precisely, we have blocks. , where and . is the largest order of the elementary Jordan 2.7 Linear Stability Let The solution of , is , and each component is a sum of terms proportional to an exponential , for an eigenvalue of . The real parts of these eigenvalues determine whether the terms are exponentially growing or decaying. Denote the generalized eigenvectors and define is the unstable eigenspace, is the center eigenspace and is the stable eigenspace. According to Lemma 2.5 each of the generalized eigen...
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## This document was uploaded on 02/24/2014 for the course MATH 512 at Washington State University .

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