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Student[VectorCalculus]

 Norm
 compute the norm of a Vector or vector field

 Calling Sequence Norm(f, p)

Parameters

 f - Vector; specify the Vector or vector field p - (optional) non-negative number, infinity, or Euclidean; specify the norm

Description

 • 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 menu, the result will be Norm(Vector(vf)) rather than Norm(vf), as this results in a more readable expression.

Examples

 > $\mathrm{with}\left(\mathrm{Student}\left[\mathrm{VectorCalculus}\right]\right):$
 > $\mathrm{Norm}\left(⟨3,4⟩\right)$
 ${5}$ (1)
 > $\mathrm{Norm}\left(⟨3,4⟩,1.5\right)$
 ${5.584250376}$ (2)

For vector fields, the Norm command returns a procedure.

 > $n≔\mathrm{Norm}\left(\mathrm{VectorField}\left(⟨xy,\frac{x}{y}⟩\right),3\right):$
 > $n\left(⟨2,3⟩\right)$
 $\frac{{2}{}{{730}}^{{1}}{{3}}}}{{3}}$ (3)
 > $\mathrm{Norm}\left(⟨2,0,3⟩,0\right)$
 ${2}$ (4)
 > $\mathrm{SetCoordinates}\left(\mathrm{spherical}\left[r,\mathrm{\phi },\mathrm{\theta }\right]\right)$
 ${{\mathrm{spherical}}}_{{r}{,}{\mathrm{\phi }}{,}{\mathrm{\theta }}}$ (5)
 > $\mathrm{Norm}\left(⟨1,\frac{\mathrm{\pi }}{2},\frac{\mathrm{\pi }}{3}⟩,\mathrm{Euclidean}\right)$
 ${1}$ (6)
 > $\mathrm{Norm}\left(⟨2,\frac{\mathrm{\pi }}{3},\frac{\mathrm{\pi }}{4}⟩,\mathrm{\infty }\right)$
 $\frac{\sqrt{{6}}}{{2}}$ (7)