Hilbert Space
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A Hilbert space is a vector space that has a complete inner product. Hilbert spaces are important in the study of infinite-dimensional vector spaces.
Hilbert space is a college-level concept that would be first encountered in an analysis course covering functional analysis.
Prerequisites
| Inner Product: | (1) In a vector space, an inner product is a way to multiply vectors together, with the result being a scalar. (2) In vector algebra, the term inner product is used as a synonym for dot product. |
| Vector Space: | A vector space is a set that is closed under finite vector addition and scalar multiplication. The basic example is n-dimensional Euclidean space. |