IEC 60050 - International Electrotechnical Vocabulary


IEVref:	102-03-47	ID:
Language:	en	Status: Standard

Term:	inner product, <of a tensor and a vector>
Synonym1:	contracted product, <of a tensor and a vector> [Preferred]
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Definition:	for a tensor of the second order $T = (T_{i j})$ and a vector U = (U_k), vector the components of which are given by ${(T \cdot U)}_{i} = \sum_{m} T_{i m} U_{m}$ 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 $D = \vec{\vec{ε}} \cdot E$ between the electric field strength E and the electric flux density D, where $\vec{\vec{ε}}$ 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
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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 </i> and </sub> tags. LMO
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