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Let V be an inner product space with an orthonormal basis B {V?, V2,..., Vn}....

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Algebra

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Let V be an inner product space with an orthonormal basis B {V?, V2,..., Vn}. Let v = a?v? + a?V?+...+anVn and w = b?V?+b?V2+...+bnVn. Prove (v, w) = a?b?+a?b2+...+anbn.

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Transcribed Image Text

Let V be an inner product space with an orthonormal basis B {V?, V2,..., Vn}. Let v = a?v? + a?V?+...+anVn and w = b?V?+b?V2+...+bnVn. Prove (v, w) = a?b?+a?b2+...+anbn.

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