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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.

'''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.

[[Category:Mathematics]]

[[Category:Mathematics]]