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Unformatted text preview: ion Theorem, is given by
If is an is nilpotent of order matrix of form  and is a real eigenvalue of then where and , …. Then . Similarly, if
of , then is an matrix of form  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  leads to the following result.
Corollary. Each coordinate in the solution
combination of functions of form
where of the initial value problem  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
The solution of
, 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
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 .
- Fall '14