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VectorCalculus[Norm] - compute the norm of a Vector or vector field
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Calling Sequence
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Norm(v, p)
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Parameters
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v
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Vector(algebraic); Vector whose norm is computed
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p
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(optional) nonnegative, infinity, or identical(Euclidean); the norm to compute
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Description
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The Norm(v, p) command computes the p-norm of the Vector or vector field v. If p is omitted, it defaults to 2.
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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.
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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.
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The 2-norm can also be specified using the value Euclidean for the parameter p.
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If  , then the value computed by this command defines a metric, but not a norm. See LinearAlgebra[Norm] for details.
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Examples
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![SetCoordinates(cartesian[x, y])](/support/helpjp/helpview.aspx?si=4012/file03390/math129.png)
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![SetCoordinates(cartesian[x, y, z])](/support/helpjp/helpview.aspx?si=4012/file03390/math151.png)
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![SetCoordinates(spherical[r, phi, theta])](/support/helpjp/helpview.aspx?si=4012/file03390/math162.png)
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![Norm(PositionVector([1, (1/2)*Pi, (1/3)*Pi]), Euclidean)](/support/helpjp/helpview.aspx?si=4012/file03390/math166.png)
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![Norm(PositionVector([2, (1/3)*Pi, (1/4)*Pi]), infinity)](/support/helpjp/helpview.aspx?si=4012/file03390/math173.png)
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![SetCoordinates(polar[r, theta])](/support/helpjp/helpview.aspx?si=4012/file03390/math180.png)
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![Norm(RootedVector(root = [1, 2], [a, b]))](/support/helpjp/helpview.aspx?si=4012/file03390/math184.png)
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| (6) |
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