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VectorCalculus

  

Normalize

  

normalize a Vector or vector field

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

Normalize(v, p)

Parameters

v

-

Vector(algebraic); Vector to be normalized

p

-

(optional) nonnegative, infinity, or identical(Euclidean); the norm to use

Description

• 

The Normalize(v, p) command normalizes the Vector or vector field v with respect to the p-norm.  If p is omitted, it defaults to 2.

• 

If v is a RootedVector, it is normalized 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.

• 

The 2-norm can also be specified using the value Euclidean for the parameter p.

• 

If the p-norm of the input Vector v is 0, then v is returned.

Examples

withVectorCalculus:

SetCoordinatescartesianx,y:

Normalize3,4

35ex+45ey

(1)

nNormalizeVectorFieldxy,xy,3

nxyyxy6+113e_x+xyxyy6+113e_y

(2)

simplifyevalVFn,2,3

97302373073023730

(3)

SetCoordinatescartesianx,y,z:

Normalize2,0,3,0

1ex+0ey+32ez

(4)

SetCoordinatessphericalr,φ,θ:

NormalizePositionVector1,Pi2,Pi3,Euclidean

12320

(5)

vNormalizePositionVector2,Pi3,Pi4,∞

v1163

(6)

Normv,∞

1

(7)

SetCoordinatespolarr,θ:

NormalizeRootedVectorroot=1,2,a,b

aa2+b2ba2+b2

(8)

See Also

LinearAlgebra[Norm]

Physics

PositionVector

RootedVector

Vector

VectorCalculus

VectorCalculus details

VectorCalculus[Norm]

VectorCalculus[SetCoordinates]

VectorField