Norm - Maple Help
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VectorCalculus

  

Norm

  

compute the norm of a Vector or vector field

 

Calling Sequence

Parameters

Description

Examples

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 0p<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

withVectorCalculus&colon;

SetCoordinatescartesianx,y&colon;

Norm3&comma;4

5

(1)

nNormVectorFieldxy&comma;xy&comma;3&colon;

n2&comma;3

2730133

(2)

SetCoordinatescartesianx,y,z&colon;

Norm2&comma;0&comma;3&comma;0

2

(3)

SetCoordinatessphericalr,φ,θ&colon;

NormPositionVector1&comma;π2&comma;π3&comma;Euclidean

1

(4)

NormPositionVector2&comma;π3&comma;π4&comma;

62

(5)

SetCoordinatespolarr,θ&colon;

NormRootedVectorroot=1&comma;2&comma;a&comma;b

a2+b2

(6)

See Also

LinearAlgebra[Norm]

Physics

PositionVector

RootedVector

Vector

VectorCalculus

VectorCalculus details

VectorCalculus[Normalize]

VectorCalculus[SetCoordinates]

VectorField

 


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