|Definition:|| for any vector U, non-negative scalar, usually denoted by , equal to the non-negative square root of the scalar product or, in the case of a complex vector, of the Hermitian product of the vector by itself|
Note 1 to entry: The magnitude of a vector U has the following properties:
- if and only if ,
- where α is a scalar,
- where V is any other vector.
Note 2 to entry: For a vector U in the three-dimensional Euclidean or Hermitian space with orthonormal base, the magnitude is given by .
Note 3 to entry: The terms "Euclidean norm" and "Hermitian norm" may be used for the real or the complex case, respectively.
Note 4 to entry: The magnitude of a vector U is represented by or by U; is also used.