compute the norm of a Vector or vector field - Maple Help

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Student[VectorCalculus][Norm] - compute the norm of a Vector or vector field

Calling Sequence

Norm(f, p)

Parameters

f

-

Vector; specify the Vector or vector field

p

-

(optional) non-negative number, infinity, or Euclidean; specify the norm

Description

• 

The Norm(f, p) calling sequence computes the p-norm  of the Vector or vector field f. If p is omitted, it defaults to 2.

  

Note: If the current coordinate system (see SetCoordinates) is not cartesian, the Vector is transformed to Cartesian coordinates before the norm is computed (see MapToBasis).

• 

If f is a vector field, the result is a procedure that, at any point (Vector) v, evaluates to the p-norm of the value of f at v.

• 

The Norm(f,Euclidean) calling sequence is equivalent to Norm(f,2).

• 

If 0<=p<1 the value computed by this command defines a metric , but not a norm . For more information, see LinearAlgebra[Norm].

• 

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

withStudent&lsqb;VectorCalculus&rsqb;&colon;

Norm3&comma;4

5

(1)

Norm3&comma;4&comma;1.5

5.584250376

(2)

For vector fields, the Norm command returns a procedure.

n:=NormVectorFieldxy&comma;xy&comma;3&colon;

n2&comma;3

237301&sol;3

(3)

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

2

(4)

SetCoordinatessphericalr&comma;&phi;&comma;&theta;

sphericalr&comma;&phi;&comma;&theta;

(5)

Norm1&comma;&pi;2&comma;&pi;3&comma;Euclidean

1

(6)

Norm2&comma;&pi;3&comma;&pi;4&comma;&infin;

1232

(7)

See Also

LinearAlgebra[Norm], Student[VectorCalculus], Student[VectorCalculus][MapToBasis], Student[VectorCalculus][Normalize], Student[VectorCalculus][SetCoordinates], Student[VectorCalculus][Vector], Student[VectorCalculus][VectorField]


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