IEVref: 102-03-17 ID: Language: en Status: Standard Term: scalar product Synonym1: dot product [Preferred] Synonym2: Synonym3: Symbol: Definition: scalar, denoted by $U\cdot V$, attributed to any pair of vectors U and V in a vector space by a given bilinear form, with the following properties: symmetry: $U\cdot V=V\cdot U$, $U\cdot U>0$ for $U\ne 0$Note 1 to entry: In an n-dimensional space with orthonormal base vectors the scalar product of two vectors U and V is the sum of the products of each coordinate ${U}_{i}$ of the vector U and the corresponding coordinate ${V}_{i}$ of the vector V: $U\cdot V=\sum _{i}{U}_{i}{V}_{i}$ Note 2 to entry: For two complex vectors U and V either the scalar product $U\cdot V$ or a Hermitian product $U\cdot V*$ may be used depending on the application. Note 3 to entry: A scalar product can be similarly defined for a pair consisting of a polar vector and an axial vector and is then a pseudo-scalar, or for a pair of two axial vectors and is then a scalar. Note 4 to entry: The scalar product of two vector quantities is the scalar product of the associated unit vectors multiplied by the product of the scalar quantities. Note 5 to entry: The scalar product is denoted by a half-high dot (·) between the two symbols representing the vectors. 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: replaced a ">" in 2nd bullet point with a ">". LMO CO remarks: TC/SC remarks: VT remarks: Domain1: Domain2: Domain3: Domain4: Domain5: