Kunze Linear Algebra · Problem 8.1.9

Inner Product Spaces

Mathematics — Methods · inner-products-quadratic-form

Problem

Let VV be a real or complex vector space with an inner product. Show that the quadratic form determined by the inner product satisfies the parallelogram law ∥α+β∥2+∥α−β∥2=2∥α∥2+2∥β∥2.\|\alpha + \beta\|^2 + \|\alpha - \beta\|^2 = 2\|\alpha\|^2 + 2\|\beta\|^2.

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