# Requirements for $\mathbf Q = \mathbf P\cdot\mathbf Q^T\cdot\mathbf P^T$

Say I have a known matrix $\mathbf Q$, outer product of 2 vectors. What kind of matrix $\mathbf P$ do I need for the following statement to be true?

$$\mathbf Q = \mathbf P\cdot\mathbf Q^T\cdot\mathbf P^T$$

Thank you very much.