Thread: Specific case of Jordan normal form

I'm having trouble understanding Jordan normal form for matrices. I can prove it works for 3x3, but the general proof is a bit over my head, so I figured I'd try the 4x4 case. But even the really easy case, where matrix A has a single eigenvalue x and eigenspace of dimension 1, I can't prove it.

Obviously the Jordan normal form should look like:

x 1 0 0
0 x 1 0
0 0 x 1
0 0 0 x

but I'm not sure how to prove an arbitrary 4x4 matrix meeting those criteria can be put in this form.

Originally Posted by deltadesu

I'm having trouble understanding Jordan normal form for matrices. I can prove it works for 3x3, but the general proof is a bit over my head, so I figured I'd try the 4x4 case. But even the really easy case, where matrix A has a single eigenvalue x and eigenspace of dimension 1, I can't prove it.

Obviously the Jordan normal form should look like:

x 1 0 0
0 x 1 0
0 0 x 1
0 0 0 x

but I'm not sure how to prove an arbitrary 4x4 matrix meeting those criteria can be put in this form.

I'm afraid that this stuff is way to heavy and complex to explain it by this means. Look for some help in your school and if you get stuck in some particular detail then you can ask here.

Tonio