Parseval's identity
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In functional analysis, a branch of mathematics, 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 a complete inner-product space (i.e. a Hilbert space), then
The origin of the name is in Parseval's theorem for Fourier series, which is a special case.
Parseval's identity can be proved using the Riesz-Fischer theorem.
[edit] See also
[edit] References
- Johnson, Lee W., and R. Dean Riess (1982). Numerical Analysis, 2nd ed., Reading, Mass.: Addison-Wesley. ISBN 0-201-10392-3.
