Let V be a finite dimensional vector space over R, with a positive definite scalar product. Let {e,.e,} be an orthonormal basis for V. Let v, weV. Let [v] =X and [w]=Y be their coordinate vectors in R" with respect to this basis. Prove: = X •Y ; that is, the scalar product equals the dot product of X and Y.

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Q: Let B = {v1,...,Vn} be an orthonormal basis for R". (a) Prove Parseval's Identity, that is, for any…

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