A positive definite function is, is greatest generality, one which is strictly postiive for nonzero arguments (and zero for a zero agrument).

In quantum mechanics, an operator A is positive definite iff for all states, <p|A|p> >= 0.
An non-degenerate operator of the form B+B is always positive definite because <p|B+B |p> = <q|q>, where |q> = B|p>, and as an axiom <q|q> >= 0.