an inner product space (or, rarely, a Hausdorff pre-Hilbert space) is a real vector space or a complex vector space with an operation called an inner product...
56 KB (7,305 words) - 10:53, 26 August 2024
function spaces. Formally, a Hilbert space is a vector space equipped with an inner product that induces a distance function for which the space is a complete...
128 KB (17,487 words) - 22:34, 20 June 2024
product) of Euclidean space, even though it is not the only inner product that can be defined on Euclidean space (see Inner product space for more). Algebraically...
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indefinite inner product space ( K , ⟨ ⋅ , ⋅ ⟩ , J ) {\displaystyle (K,\langle \cdot ,\,\cdot \rangle ,J)} is an infinite-dimensional complex vector space K {\displaystyle...
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defined over a set of labels S {\displaystyle S} in an inner product space with an inner product ⟨ ⋅ , ⋅ ⟩ {\displaystyle \langle \cdot ,\cdot \rangle...
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semidirect products Product of rings Ideal operations, for product of ideals Scalar multiplication Matrix multiplication Inner product, on an inner product space...
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Square-integrable function (redirect from L2-inner product)
specifically a Hilbert space, because the space is complete under the metric induced by the inner product. This inner product space is conventionally denoted...
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inequality) is an upper bound on the inner product between two vectors in an inner product space in terms of the product of the vector norms. It is considered...
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tensor product. The tensor product allows Hilbert spaces to be collected into a symmetric monoidal category. Since Hilbert spaces have inner products, one...
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complete for this norm. An inner product space is a normed vector space whose norm is the square root of the inner product of a vector and itself. The...
18 KB (2,890 words) - 22:11, 21 February 2024