NOTE 1 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 V is any other vector.

NOTE 2 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 The terms "Euclidean norm" and "Hermitian norm" may be used for the real or the complex case, respectively.

NOTE 4 The magnitude of a vector U is represented by $\left|U\right|$ or by U; $\Vert U\Vert$ is also used.