Difference between revisions of "Hilbert Space"
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| − | Hilbert space is | + | '''Hilbert space''' is an [[inner product space]] that is also a [[complete metric space]]. A Hilbert space is always a [[Banach space]], but the converse need not hold. Hilbert space is named after mathematician [[David Hilbert]], who used it to provide a natural context in which to generalize the concept of [[Fourier series]] and [[Fourier transformation]] in terms of arbitrary orthogonal functions defined on infinite dimensional inner product space. |
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| + | [[Category:Mathematics]] | ||
Latest revision as of 00:32, May 3, 2008
Hilbert space is an inner product space that is also a complete metric space. A Hilbert space is always a Banach space, but the converse need not hold. Hilbert space is named after mathematician David Hilbert, who used it to provide a natural context in which to generalize the concept of Fourier series and Fourier transformation in terms of arbitrary orthogonal functions defined on infinite dimensional inner product space.