Let B = {v 1 ,......, v n } be an orthonormal basis for R n .
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Let B = {v1,......, vn} be an orthonormal basis for Rn.
(a) Prove that, for any x and y in Rn, x • y = (x • v1) (y • v1) + (x • v2) (y • v2) + ...........+ (x • vn) (y • vn) (This identity is called Parseval’s Identity.)
(b) What does Parseval’s Identity imply about the relationship between the dot products x • y and [x]B • [y]B?
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