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Jordan decomposition
Posted: Thu Mar 25, 2010 11:56 am
by luxu1983
dear
how can i do Jordan decomposition，if i have matrix a ||1,3|3,2||?
thank you very much
Re: Jordan decomposition
Posted: Thu Mar 25, 2010 12:19 pm
by TomDoan
For this model, you can do that with:
Code: Select all
compute [rect] a=||1,3|3,2||
eigen a eigval eigvect
disp eigvect*%diag(eigval)*inv(eigvect)
Your input matrix has real eigenvalues with no repeats. For complex eigenvalues with no repeats, you can use EIGEN with the CVECTOR and CVALUE options to get the complex eigenvectors and eigenvalues. If you have a matrix which isn't diagonalizable (repeated eigenvalues with a deficient rank eigenspace), RATS doesn't offer a way to get the Jordan form. However, that's not an interesting case practically, since repeated eigenvalues are unlikely in practice except when forced explicitly, like a double unit root.