Parseval's identity

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In functional analysis, Parseval's identity aka Parseval's equality is the Pythagorean theorem of inner-product spaces. Given an orthonormal basis B,

<math>\|x\|^2=\langle x,x\rangle=\sum_{v\in B}\langle x,v\rangle^2<math>.

The origin of the name is in Parseval's theorem for Fourier series, which is a special case.

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