compute the norm of a Vector or vector field
Vector(algebraic); Vector whose norm is computed
(optional) nonnegative, infinity, or identical(Euclidean); the norm to compute
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 0≤p<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.
n ≔ Norm⁡VectorField⁡x⁢y,xy,3:
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