Norm - Maple Help

VectorCalculus

 Norm
 compute the norm of a Vector or vector field

 Calling Sequence Norm(v, p)

Parameters

 v - Vector(algebraic); Vector whose norm is computed p - (optional) nonnegative, infinity, or identical(Euclidean); the norm to compute

Description

 • The Norm(v, p) command computes the p-norm of the Vector or vector field v. If p is omitted, it defaults to 2.
 • If v is a RootedVector, its norm is computed in the corresponding vector space, that is, relative to the root point of that vector space.  See VectorCalculus details for more information about rooted vectors.
 • If v is a vector field, the result is a procedure which at any point (Vector) w evaluates to the p-norm of the value of v at w.
 • The 2-norm can also be specified using the value Euclidean for the parameter p.
 • If $0\le p<1$ , then the value computed by this command defines a metric, but not a norm.  See LinearAlgebra[Norm] for details.
 • 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

 > $\mathrm{with}\left(\mathrm{VectorCalculus}\right):$
 > $\mathrm{SetCoordinates}\left({\mathrm{cartesian}}_{x,y}\right):$
 > $\mathrm{Norm}\left(⟨3,4⟩\right)$
 ${5}$ (1)
 > $n≔\mathrm{Norm}\left(\mathrm{VectorField}\left(⟨xy,\frac{x}{y}⟩\right),3\right):$
 > $n\left(⟨2,3⟩\right)$
 $\frac{{2}{}{{730}}^{{1}}{{3}}}}{{3}}$ (2)
 > $\mathrm{SetCoordinates}\left({\mathrm{cartesian}}_{x,y,z}\right):$
 > $\mathrm{Norm}\left(⟨2,0,3⟩,0\right)$
 ${2}$ (3)
 > $\mathrm{SetCoordinates}\left({\mathrm{spherical}}_{r,\mathrm{φ},\mathrm{θ}}\right):$
 > $\mathrm{Norm}\left(\mathrm{PositionVector}\left(\left[1,\frac{\mathrm{Pi}}{2},\frac{\mathrm{Pi}}{3}\right]\right),\mathrm{Euclidean}\right)$
 ${1}$ (4)
 > $\mathrm{Norm}\left(\mathrm{PositionVector}\left(\left[2,\frac{\mathrm{Pi}}{3},\frac{\mathrm{Pi}}{4}\right]\right),\mathrm{∞}\right)$
 $\frac{\sqrt{{6}}}{{2}}$ (5)
 > $\mathrm{SetCoordinates}\left({\mathrm{polar}}_{r,\mathrm{θ}}\right):$
 > $\mathrm{Norm}\left(\mathrm{RootedVector}\left(\mathrm{root}=\left[1,2\right],\left[a,b\right]\right)\right)$
 $\sqrt{{{a}}^{{2}}{+}{{b}}^{{2}}}$ (6)