Question: Let C = [Cij] be an n x n positive definite symmetric matrix and let V be an n-dimensional vector space with ordered basis S

Let C = [Cij] be an n x n positive definite symmetric matrix and let V be an n-dimensional vector space with ordered basis S = {u1, u2,... un}. For v = a1u1+ a2u2+...+anun and w = b1u1+b2u2+ ... + bnun in V define

Prove that this defines an inner product on V.

aiCijbi

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