Hilbert space

In mathematics, a Hilbert space is an inner product space that is complete with respect to the norm defined by the inner product. Hilbert spaces serve to clarify and generalize the concept of Fourier expansion and certain linear transformations such as the Fourier transform. Hilbert spaces are of crucial importance in the mathematical formulation of quantum mechanics, although many basic features of quantum mechanics can be understood without going into details about Hilbert spaces. Hilbert spaces are studied in functional analysis.

Related Topics:
Mathematics - Inner product space - Complete - Norm - Fourier expansion - Linear transformation - Fourier transform - Quantum mechanics - Functional analysis

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