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(b) Prove that such a T maps orthonormal sets in V to orthonormal sets in W. Is this true for an
isomorphism in general?
(c) Prove that if W is Euclidean n-space and if , then there is an inner product space
isomorphism between V and W.
(d) Use the result of part (c) to prove that if , then there is an inner product
space isomorphism between V and W.
(e) Find an inner product space isomorphism between and .
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