The Norm(f, p) calling sequence computes the p-norm of the Vector or vector field f. If p is omitted, it defaults to 2.

Note: If the current coordinate system (see SetCoordinates) is not cartesian, the Vector is transformed to Cartesian coordinates before the norm is computed (see MapToBasis).

If f is a vector field, the result is a procedure that, at any point (Vector) v, evaluates to the p-norm of the value of f at v.

The Norm(f,Euclidean) calling sequence is equivalent to Norm(f,2).

If $0<=p<1$ the value computed by this command defines a metric, but not a norm. For more information, see LinearAlgebra[Norm].

Note: If the Norm command is applied to a vector field, vf, using the Context Panel, the result will be Norm(Vector(vf)) rather than Norm(vf), as this results in a more readable expression.

$\mathrm{with}\left(\mathrm{Student}\left[\mathrm{VectorCalculus}\right]\right)\&colon;$

$\mathrm{Norm}\left(⟨3\&comma;4⟩\right)$

$5$

$\mathrm{Norm}\left(⟨3\&comma;4⟩\&comma;1.5\right)$

$5.584250376$

$n≔\mathrm{Norm}\left(\mathrm{VectorField}\left(⟨xy\&comma;\frac{x}{y}⟩\right)\&comma;3\right)\&colon;$

$n\left(⟨2\&comma;3⟩\right)$

$\frac{2{730}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}}{3}$

$\mathrm{Norm}\left(⟨2\&comma;0\&comma;3⟩\&comma;0\right)$

$2$

$\mathrm{SetCoordinates}\left(\mathrm{spherical}\left[r,\mathrm{\phi },\mathrm{\theta }\right]\right)$

${\mathrm{spherical}}_{r,\mathrm{\phi },\mathrm{\theta }}$

$\mathrm{Norm}\left(⟨1\&comma;\frac{\mathrm{\pi }}{2}\&comma;\frac{\mathrm{\pi }}{3}⟩\&comma;\mathrm{Euclidean}\right)$

$1$

$\mathrm{Norm}\left(⟨2\&comma;\frac{\mathrm{\pi }}{3}\&comma;\frac{\mathrm{\pi }}{4}⟩\&comma;\mathrm{\infty }\right)$

$\frac{\sqrt{6}}{2}$