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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
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.
. The generalized eigenspace associated
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
We are now ready to find
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
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