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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

n:=xyx3y3+x3y31/3e_x+xx3y3+x3y31/3ye_y

(2)

simplifyevalVFn,2,3

97307302/317307302/3

(3)

SetCoordinatescartesianx,y,z:

Normalize2,0,3,0

ex+32ez

(4)

SetCoordinatessphericalr,φ,θ:

NormalizePositionVector1,π2,π3,Euclidean

121230

(5)

vNormalizePositionVector2,π3,π4,∞

v:=111332

(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

 


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