Vector Space Let a vector space VVV be a Set of Vector with addition such that ∣u⟩+∣v⟩∈V;∣u⟩,∣v⟩∈V\begin{gather*} \left\lvert u \right\rangle+\left\lvert v \right\rangle\in V\quad ;\quad\left\lvert u \right\rangle,\left\lvert v \right\rangle\in V \end{gather*}∣u⟩+∣v⟩∈V;∣u⟩,∣v⟩∈V scalar multiplication such that Hilbert Space