Change of basis to a nonnegative matrix

Question

Let $A$ be an arbitrary symmetric, square matrix. I would like to use the Perron-Frobenius theorem, but I cannot do that directly since $A$ is not necessarily a non-negative matrix. So I had the following idea: find a change-of-basis matrix $U$ such that $B:=UAU^{-1}$ is non-negative, apply the Perron-Frobenius theorem to $B$, and undo the change of basis. However, I do not know if this is for any matrix $A$ such a matrix $U$ exists; or if there are some necessary conditions on $A$ for $U$ to exist. Moreover, I cannot think of any method to get $U$.