Find the Jordan Canonical form of the following matrice:
For this one, here is what I have so far:
First, I found the eigenvalues are 1 and 2, and the basis of eigenvectors are
Now, I know I have to find , but I'm bit rusty on this, I can't remember how to do it, any hint, please?
Fot the above matrix A, each eigenvalue has an eigenspace of dimension 1 (an eigenvector for the eigenvalue 2 must be a multiple of (1,0,0,0) and an eigenvector for the eigenvalue 3 must be a multiple of (0,0,0,1)). So the JCF looks like .
Thanks, but I cannot understand why the the eigenvectors are such, let me show you how I worked mine, please correct me.
The eigenvalues are -1 and 4, so the eigenspace for -1 is:
So I have to solve
Let , we have , so the eigenvectors for this is
But appearly it is not, what am I doing wrong here?