Question: can you explain how to do it with proof Let V be an inner product space with inner product (., .), and let SE C(V)

can you explain how to do it with proof

Let V be an inner product space with inner product (., .), and let SE C(V) be an operator. Define a function (., .)s by the rule (v, w)s = (Sv, Sw). (a) Show that if S is injective then (, .)s is an inner product on V. (b) Show that if S is not injective then (., .)s is not an inner product on V

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