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Student[VectorCalculus]

 Normalize
 normalize a Vector or vector field

 Calling Sequence Normalize(f, p)

Parameters

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

Description

 • The Normalize(f, p) calling sequence normalizes the Vector or vector field f with respect to the p-norm. If p is omitted, it defaults to 2.  Note that if the current coordinate system (see SetCoordinates) is not cartesian, the Vector will be transformed to cartesian coordinates before the normalization is computed (see MapToBasis), and then the result will be mapped back to its original coordinate system.
 • If f is a vector field, the result is again a vector field that, at any point (Vector) v, evaluates to the normalized (with respect to the {p}-norm) value of f at v.
 • The Normalize(f,Euclidean) calling sequence is equivalent to Normalize(f,2).

Examples

 > $\mathrm{with}\left(\mathrm{Student}[\mathrm{VectorCalculus}]\right):$
 > $\mathrm{Normalize}\left(⟨3,4⟩\right)$
 $\left(\frac{{3}}{{5}}\right){{e}}_{{x}}{+}\left(\frac{{4}}{{5}}\right){{e}}_{{y}}$ (1)
 > $\mathrm{Normalize}\left(⟨3,4⟩,1.5\right)$
 $\left({0.537225195600000}\right){{e}}_{{x}}{+}\left({0.716300260800000}\right){{e}}_{{y}}$ (2)
 > $\mathrm{Normalize}\left(⟨3,4⟩,0\right)$
 $\left(\frac{{3}}{{2}}\right){{e}}_{{x}}{+}{2}{{e}}_{{y}}$ (3)

For vector fields, the Normalize command returns a vector field.

 > $n≔\mathrm{Normalize}\left(\mathrm{VectorField}\left(⟨xy,\frac{x}{y}⟩\right),3\right):$
 > $\mathrm{evalVF}\left(n,⟨2,3⟩\right)$
 $\left[\begin{array}{c}\frac{{3}}{{2920}}{}{{5840}}^{{2}{/}{3}}{}{{27}}^{{1}{/}{3}}\\ \frac{{1}}{{8760}}{}{{5840}}^{{2}{/}{3}}{}{{27}}^{{1}{/}{3}}\end{array}\right]$ (4)
 > $\mathrm{SetCoordinates}\left({\mathrm{spherical}}_{r,\mathrm{φ},\mathrm{θ}}\right)$
 ${{\mathrm{spherical}}}_{{r}{,}{\mathrm{φ}}{,}{\mathrm{θ}}}$ (5)
 > $p≔\mathrm{RootedVector}\left(\left[1,1,2\right],\mathrm{root}=⟨1,\frac{\mathrm{π}}{2},\frac{\mathrm{π}}{3}⟩\right)$
 ${p}{≔}\left[\begin{array}{r}{1}\\ {1}\\ {2}\end{array}\right]$ (6)
 > $\mathrm{Normalize}\left(p,\mathrm{Euclidean}\right)$
 $\left[\begin{array}{c}\frac{{1}}{{6}}{}\sqrt{{6}}\\ \frac{{1}}{{6}}{}\sqrt{{6}}\\ \frac{{1}}{{3}}{}\sqrt{{6}}\end{array}\right]$ (7)
 > $\mathrm{Normalize}\left(p,\mathrm{∞}\right)$
 $\left[\begin{array}{c}\frac{{1}}{{2}}\\ \frac{{1}}{{2}}\\ {1}\end{array}\right]$ (8)