projection-valued measure

Summary

projection-valued measure ranks in the top 2% of general entities by monthly Wikipedia readership (77 views/month).^[1]

Key Facts

• projection-valued measure's subclass of is recorded as positive-operator-valued measure^[2].
• projection-valued measure's Freebase ID is recorded as /m/0417yr^[3].
• projection-valued measure's short name is recorded as {'lang': 'en', 'text': 'PVM'}^[4].
• projection-valued measure's defining formula is recorded as \begin{aligned}&\pi\colon M\to B(H)\&\forall E\in M\colon\pi(E)^2=\pi(E)=\pi(E)^\dagger\&\pi(X)=\operatorname{id}H\&\pi(\varnothing)=0_H\&\forall E\in M^{\mathbb N},x\in H\colon\left(\forall i\ne j\colon E_i\cap E_j=\varnothing\right)\implies\left\lang\pi\left(\bigcup{i=0}^\infty E_i\right)x,x\right\rang=\sum_{i=0}^\infty\lang\pi(E_i)x,x\rang\end{aligned}^[5].
• projection-valued measure's maintained by WikiProject is recorded as WikiProject Mathematics^[6].
• projection-valued measure's Microsoft Academic ID is recorded as 28502450^[7].
• projection-valued measure's in defining formula is recorded as (X,M)^[8].
• projection-valued measure's in defining formula is recorded as \pi^[9].
• projection-valued measure's in defining formula is recorded as H^[10].
• projection-valued measure's in defining formula is recorded as B(H)^[11].
• projection-valued measure's in defining formula is recorded as M^[12].
• projection-valued measure's in defining formula is recorded as X^[13].
• projection-valued measure's in defining formula is recorded as \operatorname{id}^[14].
• projection-valued measure's in defining formula is recorded as \langle,\rangle^[15].
• projection-valued measure's in defining formula is recorded as ^\dagger^[16].

Why It Matters

projection-valued measure ranks in the top 2% of general entities by monthly Wikipedia readership (77 views/month).^[1] It has Wikipedia articles in 12 language editions, a strong signal of global cultural recognition.^[17]