Question: Suppose that V is an inner product space and L: V V is an isometry, so ||L[v]|| = ||v|| for all v V.

Suppose that V is an inner product space and L: V → V is an isometry, so ||L[v]|| = ||v|| for all v ∈ V. Prove that L also preserves the inner product: (L[v], L[w]) = (v, w).

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