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Hilbert Spaces - UCSD Mathematics | Home

The orthogonal projection of Honto Mis the function PM: H→Hsuch that for x∈H,PM(x) is the unique element in Msuch that (x−PM(x)) ⊥M. Proposition 12.13. Let Hbe a Hilbert space and M⊂Hbeaclosedsubspace. The orthogonal projection PMsatisfies: (1) PMis linear (and hence we will write PMxrather than PM(x). (2) P2 M= PM(PMisaprojection ...

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