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

Online Help

All Products    Maple    MapleSim


Home : Support : Online Help : Mathematics : Vector Calculus : VectorCalculus/Norm

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

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&comma;y&colon;

Norm3&comma;4

5

(1)

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

n2&comma;3

237301&sol;3

(2)

SetCoordinatescartesianx&comma;y&comma;z&colon;

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

2

(3)

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

NormPositionVector1&comma;&pi;2&comma;&pi;3&comma;Euclidean

1

(4)

NormPositionVector2&comma;&pi;3&comma;&pi;4&comma;&infin;

1232

(5)

SetCoordinatespolarr&comma;&theta;&colon;

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

a2&plus;b2

(6)

See Also

LinearAlgebra[Norm], Physics, PositionVector, RootedVector, Vector, VectorCalculus, VectorCalculus details, VectorCalculus[Normalize], VectorCalculus[SetCoordinates], VectorField


Download Help Document

Was this information helpful?



Please add your Comment (Optional)
E-mail Address (Optional)
What is ? This question helps us to combat spam