# Inner Product Space, Finite Dimensional Subspace, Orthonormal Basis and Orthogonal Projections

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Let V be an inner product space and W ⊂ V be a finite dimensional space with ONB {u1...u2}. For every x Є V

define P(x) =Σ i=1-->n <x,ui>ui

i) Prove that x-P(x)ЄW

ii) Prove that P is the orthogonal projection of W.

iii)...

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Let be an inner product space and a finite dimensional subspace with orthogonal basis ...

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Inner Product Space, Finite Dimensional Subspace, Orthonormal Basis and Orthogonal Projections are investigated.

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