repeated eigenvalues?

[mathrocks]

I'm trying to find the basis for a particular matrix and I get a 3 eigenvalues with two of them being identical to each other. What do I do to find the basis for the repeated eigenvalue? Will it have the same basis as the original number?

Thanks!

[matt grime]

The eigenvectors may or may not span the original space. That is there may only be two eigenvectors. If you solve as usual for the eigenvector you may obtain two linearly independent vectors for it (the repeated eigenvalue) or you may only get one.

If you want the geometric interpetation of this then you need to learn about Jordan Normal Form, or Jordan Canonical Form.