Hilbert Space
A hilbert space uses the mathematics of two and three dimensions to try and describe what happens in greater than three dimensions.
Hilbert space. A hilbert space is a mathematical concept covering the extra dimensional use of euclidean space i e a space with more than three dimensions. Hilbert spaces serve to clarify and generalize the concept of fourier expansion and certain linear transformations such as the fourier transform. A hilbert space is a vector space v v equipped with an inner product which can be thought of as a generalization of the dot product in euclidean space with the additional property that the metric coming from the inner product makes v v into a complete metric space.
The basic example of a hilbert space is. A hilbert space is an abstract vector space possessing the structure of an inner product that allows length and angle to be measured. Furthermore hilbert spaces are complete.
Hilbert space in mathematics an example of an infinite dimensional space that had a major impact in analysis and topology. It is named after david hilbert.