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VectorCalculus[Normalize] - normalize a Vector or vector field
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Calling Sequence
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Normalize(v, p)
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Parameters
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v
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Vector(algebraic); Vector to be normalized
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p
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(optional) nonnegative, infinity, or identical(Euclidean); the norm to use
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Description
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The Normalize(v, p) command normalizes the Vector or vector field v with respect to the p-norm. If p is omitted, it defaults to 2.
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If v is a RootedVector, it is normalized 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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The 2-norm can also be specified using the value Euclidean for the parameter p.
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If the p-norm of the input Vector v is 0, then v is returned.
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Examples
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![SetCoordinates(cartesian[x, y])](/support/helpjp/helpview.aspx?si=4289/file03391/math107.png)
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![Vector[column]([[3/5], [4/5]], ["x", "y"])](/support/helpjp/helpview.aspx?si=4289/file03391/math114.png)
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+abs(x^3/y^3))^(1/3)], [x/((abs(x^3*y^3)+abs(x^3/y^3))^(1/3)*y)]], ["x", "y"], "field")](/support/helpjp/helpview.aspx?si=4289/file03391/math121.png)
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*730^(2/3)], [(1/730)*730^(2/3)]])](/support/helpjp/helpview.aspx?si=4289/file03391/math128.png)
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![SetCoordinates(cartesian[x, y, z])](/support/helpjp/helpview.aspx?si=4289/file03391/math132.png)
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![Vector[column]([[1], [0], [3/2]], ["x", "y", "z"])](/support/helpjp/helpview.aspx?si=4289/file03391/math139.png)
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![SetCoordinates(spherical[r, phi, theta])](/support/helpjp/helpview.aspx?si=4289/file03391/math143.png)
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![Normalize(PositionVector([1, (1/2)*Pi, (1/3)*Pi]), Euclidean)](/support/helpjp/helpview.aspx?si=4289/file03391/math147.png)
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*3^(1/2)], [0]])](/support/helpjp/helpview.aspx?si=4289/file03391/math150.png)
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![v := Normalize(PositionVector([2, (1/3)*Pi, (1/4)*Pi]), infinity)](/support/helpjp/helpview.aspx?si=4289/file03391/math154.png)
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*3^(1/2)*2^(1/2)]])](/support/helpjp/helpview.aspx?si=4289/file03391/math157.png)
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| (7) |
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![SetCoordinates(polar[r, theta])](/support/helpjp/helpview.aspx?si=4289/file03391/math168.png)
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![Normalize(RootedVector(root = [1, 2], [a, b]))](/support/helpjp/helpview.aspx?si=4289/file03391/math172.png)
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^(1/2)], [b/(a^2+b^2)^(1/2)]])](/support/helpjp/helpview.aspx?si=4289/file03391/math175.png)
| (8) |
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