| scalar, denoted by , attributed to any pair of vectors U and V in a vector space by a given bilinear form, with the following properties: |
- symmetry: ,
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 of the vector U and the corresponding coordinate of the vector V:
Note 2 to entry: For two complex vectors U and V either the scalar product or a Hermitian product 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.