  In this note, for any two orthogonal projection $P,Q$ on a Hilbert space, the
characterization of spectrum of anticommutator $PQ+QP$ has been obtained. As a
corollary, the norm formula $$\parallel PQ+QP\parallel=\parallel
PQ\parallel+\parallel PQ\parallel^2$$ has been got an alternative proof (see
Sam Waltrs, Anticommutator norm formula for projection operators,
arXiv:1604.00699vl [math.FA] 3 Apr 2016)
