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Parseval's identity

In functional analysis, Parseval's identity, also known as Parseval's equality, is the Pythagorean theorem for inner-product spaces. It states that if B is an orthonormal basis in an inner-product space, then

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

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

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Last updated: 05-07-2005 01:59:02
Science Fair Project Encyclopedia Contents Page
10-26-2009 08:16:03
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