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Unformatted text preview: line solution is obtained, where is the eigenvector associated with . However the full phase portrait is most easily visualized using
a computer.
phase portrait drawn by a computer Example. Solve the initial value problem , where . Since is upper triangular, the eigenvalues can be read off the main diagonal.
has
multiplicity
and
has multiplicity
. The generalized eigenspace associated
with is
. Find
.
A choice for generalized eigenvectors spanning
generalized eigenspace associated with is is and
. Find The .
Let . The transformation matrix is
. Notice that is block diagonal. Its inverse
is also block diagonal, with each block the
inverse of the corresponding block in
Then
.
We are now ready to find
and
Then is given by and where . Obtain
It’s easy to check . 8
Chapter 2 part B , where . The solution of the initial value problem is Jordan Form
Let
where
or . cannot always be diagonalized by a similarity
transformation, but it can always be transformed into Jordan canonical form, which giv...
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This document was uploaded on 02/24/2014 for the course MATH 512 at Washington State University .
 Fall '14
 MarcEvans

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