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

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) =&#931; i=1-->n <x,ui>ui
i) Prove that x-P(x)&#1028;W
ii) Prove that P is the orthogonal projection of W.
iii)...

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

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