Jordan decomposition

[luxu1983]

dear
how can i do Jordan decomposition，if i have matrix a ||1,3|3,2||?
thank you very much

[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.