Difference between revisions of "Hilbert Space"
Jump to navigation
Jump to search
(inner product space) |
m |
||
| Line 1: | Line 1: | ||
| − | Hilbert space is a [[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 a [[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]], whom 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. |
| + | |||
[[Category:Mathematics]] | [[Category:Mathematics]] | ||
Revision as of 01:33, March 24, 2007
Hilbert space is a 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, whom 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.