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IEVref: | 102-03-23 | ID: | |

Language: | en | Status: Standard | |

Term: | magnitude, <of a vector> | ||

Synonym1: | norm, <of a vector> | ||

Synonym2: | |||

Synonym3: | |||

Symbol: | |||

Definition: | for any vector , non-negative scalar, usually denoted by $\left|U\right|$, 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 itselfUNote 1 to entry: The magnitude of a vector - $U=0$ if and only if $\left|U\right|=0$,
- $\left|\alpha U\right|=\left|\alpha \right|\cdot \left|U\right|$ where
*α*is a scalar, - $\left|U+V\right|\le \left|U\right|+\left|V\right|$ where
is any other vector.*V*
Note 2 to entry: For a vector 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; $\Vert U\Vert $ 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: |

Note 1 to entry: The magnitude of a vector ** U** has the following properties:

- $U=0$ if and only if $\left|U\right|=0$,
- $\left|\alpha U\right|=\left|\alpha \right|\cdot \left|U\right|$ where
*α*is a scalar, - $\left|U+V\right|\le \left|U\right|+\left|V\right|$ where
is any other vector.*V*

Note 2 to entry: For a vector ** U** in the three-dimensional Euclidean or Hermitian space with orthonormal base, the magnitude is given by $\left|U\right|=\sqrt{{\left|{U}_{1}\right|}^{2}+{\left|{U}_{2}\right|}^{2}+{\left|{U}_{3}\right|}^{2}}$.

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 $\left|U\right|$ or by