Let V be an inner product space. Prove that if u and v are any vectors in V, then ||u + v||2 = ||u||2 + ||v||2 if and only if (u, v) = 0, that is, if and only if u and v are orthogonal. This result is known as the Pythagorean Theorem.

Let V be an inner product space. Prove that if u and v are any vectors in V, then ||u + v||2 = ||u||2 + ||v||2 if and only if (u, v) = 0, that is, if and only if u and v are orthogonal. This result is known as the Pythagorean Theorem.

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Related Book For answer-question

Elementary Linear Algebra with Applications

9th edition

Authors: Bernard Kolman, David Hill

ISBN: 978-0132296540