Hi. I have some questions regarding eigen-related things.

1) If A & B are similar matrices do they have the same eigenvectors? (I know they have the same eigenvalues...) If not, can someone please give an example?

2) A is a square matrix. Do A and $\displaystyle A^t$ have the same eigenvalues? Do A and $\displaystyle A^t$ have the same eigenvectors? If not can someone please give an example?

Thanks!