Question: Inner Products induce Norms Let V be a vector space, and let (., .) : V X V - R be an inner product on

Inner Products induce Norms

Let V be a vector space, and let (., .) : V X V - R be an inner product on V. Define | |x|| := (x, x). Prove that | | . | | is a norm. (Hint: To prove the triangle inequality holds, you may need the Cauchy-Schwartz inequality, (x, y)

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