Projective Hilbert space

In mathematics and the foundations of quantum mechanics, the projective Hilbert space ${\displaystyle P(H)}$ of a complex Hilbert space ${\displaystyle H}$ is the set of equivalence classes of vectors ${\displaystyle v}$ in ${\displaystyle H}$, with ${\displaystyle v\neq 0}$, for the relation ${\displaystyle \sim }$ given by

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