Originally Posted by

**ercan** I need help about similarity transformation in matrices.

Is there anyone who knows how can I decide whether "the two matrices having the same eigenvalues" are similar or not without using eigenvectors.

For example, following two matrices have the same characteristic polynomial. But they are not similar. Because matrix A has multiple jordan blocks for the double eigenvalue 1 while B doesn't have multiple jordan block.

A=[3 -3 -1 2;

4 -2 -3 6;

4 -3 -2 6;

3 0 -3 7]

B=[-4.6 -7 -3 -0.6;

3.4 6 2 0.4;

0.4 0 1 0.4;

-2.4 5 0 3.6]

I wonder how can I show that A and B are not similar without using their eigenvectors or without directly looking to their diagonal forms.