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

Spectra of anticommutator for two orthogonal projections