IEVref: 102-03-23 ID: Language: en Status: Standard Term: magnitude, Synonym1: norm, Synonym2: Synonym3: Symbol: Definition: for any vector U, non-negative scalar, usually denoted by $|U|$, 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 itselfNote 1 to entry: The magnitude of a vector U has the following properties: $U=0$ if and only if $|U|=0$, $|\alpha U|=|\alpha |\cdot |U|$ where α is a scalar, $|U+V|\le |U|+|V|$ 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 $|U|=\sqrt{{|{U}_{1}|}^{2}+{|{U}_{2}|}^{2}+{|{U}_{3}|}^{2}}$. 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 $|U|$ or by U; $‖U‖$ is also used. 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 CO remarks: TC/SC remarks: VT remarks: Domain1: Domain2: Domain3: Domain4: Domain5: