Question 4 inner product on V. Show that the following are equivalent: (1) ||v – w|| = ||S(v) – S(w)|| for all v, w E V. (i.e. S is distance preserving.) (2) (v, w) = (S(v), S(w)) for all v, w E V. (i.e. S is inner-product preserving.) Let V be a finite dimensional vector space, with S: V → V a linear operator, and (, ·) an

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