I'm really confused. If $V$ is an orthogonal matrix that transforms matrix $U_1$ into matrix $U_2$ why is it that $U_2 = V^TU_1V$?
With what I know, an orthogonal matrix is one such that $V^{-1} = V^T$:
Thus if $U_2 = VU_1$ then I cannot perceive how $U_2 = V^TU_1V$