# Help proving that matrices are similar

1. Mar 29, 2009

1. Given two 4x4 matrices, A and B, I must determine if they are similar.
A=[(2,0,0,0) B=[(5,0,-4,-7)
(-4,-1,-4,0) (3,-8,15,-13)
(2,1,3,0) (2,-4,7,-7)
(-2,4,9,1)] (1,2,-5,1)]

2. A and B are similar if, A=P^(-1)BP

3. I found the eigenvalues to be 1,1,1,2 for both matrices. I also calculated their eigenvectors and eigenspaces. I am stumped as how to show that the two are similar. I know similar matrices have the same eigenvalues, but I don't think that is enough to prove similarity.

Thanks for any help,
James

2. Mar 29, 2009

### e(ho0n3

Are you familiar with any of the canonical forms?

3. Mar 29, 2009

Yes. Would finding the smith normal form help at all?

4. Mar 29, 2009

### e(ho0n3

Sure. If they both have the same Smith normal form, then they are similar.

5. Mar 29, 2009