IEVref: 102-03-47 ID: Language: en Status: Standard Term: inner product, Synonym1: contracted product, [Preferred] Synonym2: Synonym3: Symbol: Definition: for a tensor of the second order $T=\left({T}_{ij}\right)$ and a vector U = (Uk), vector the components of which are given by ${\left(T\cdot U\right)}_{i}=\sum _{m}{T}_{im}{U}_{m}$Note 1 to entry: The inner product of two vectors is their scalar product, because a tensor of the first order is considered as a vector. Note 2 to entry: An example is the relation $D=\stackrel{\to }{\stackrel{\to }{\epsilon }}\cdot E$ between the electric field strength E and the electric flux density D, where $\stackrel{\to }{\stackrel{\to }{\epsilon }}$ is the absolute permittivity of an anisotropic medium. Note 3 to entry: The inner product of a tensor and a vector is denoted by a half-high dot (·) between the two symbols. Publication date: 2008-08 Source: Replaces: Internal notes: 2017-02-20: Editorial revisions in accordance with the information provided in C00019 (IEV 102) - evaluation. JGO 2017-08-24: Corrected order of and tags. LMO CO remarks: TC/SC remarks: VT remarks: Domain1: Domain2: Domain3: Domain4: Domain5: