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L^2-Inner Product


The L^2-inner product of two real functions f and g on a measure space X with respect to the measure mu is given by

 <f,g>_(L^2)=int_Xfgdmu,

sometimes also called the bracket product, where the symbol <f,g> are called angle brackets. If the functions are complex, the generalization of the Hermitian inner product

 int_Xfg^_dmu

is used.


See also

Angle Bracket, Bra, Hilbert Space, Inner Product, Ket, Lebesgue Integral, L2-Function, L2-Space

This entry contributed by Todd Rowland

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Cite this as:

Rowland, Todd. "L^2-Inner Product." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/L2-InnerProduct.html

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