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...

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...

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...

indefinite inner product space ( K , ⟨ ⋅ , ⋅ ⟩ , J ) {\displaystyle (K,\langle \cdot ,\,\cdot \rangle ,J)} is an infinite-dimensional complex vector space K {\displaystyle...

Mirror (2022) Priam InnerSpace, a hard disk drive series by Priam Corporation in the 1980s Inner product space, a kind of vector space in linear algebra...

tensor product. The tensor product allows Hilbert spaces to be collected into a symmetric monoidal category. Since Hilbert spaces have inner products, one...

semidirect products Product of rings Ideal operations, for product of ideals Scalar multiplication Matrix multiplication Inner product, on an inner product space...

specifically a Hilbert space, because the space is complete under the metric induced by the inner product. This inner product space is conventionally denoted...

vector space equipped with the usual dot product ⟨ ⋅ , ⋅ ⟩ {\displaystyle \langle \cdot ,\cdot \rangle } (thus making it an inner product space), and let...

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...