Let B = S^-1 * A * S and x be an eigenvector of B belonging to an eigenvalue [tex]\lambda[/tex]. Show S*x is an eigenvector of A belonging to [tex]\lambda[/tex].
The Attempt at a Solution
The only place I can think of to start, is that B*x = [tex]\lambda[/tex]*x.
However, even starting with that, I can't figure out where to go next.
Could someone point me in the right direction?