# For linear quadratic approximation of RBC model, why does matrix $P$ of value function $V = F^TPF$ has to be negative semi-definite matrix?

In http://www.compmacro.com/makoto/note/note_rbc_lq.pdf page 5, it is said that for value function $V = F^TPF$ (Bellman equation) $P$ has to be negative semi-definite matrix. Why does it have to be negative semi-definite?