Vector-Input Function

A Vector-Input Function is a tuple-input function that is a vector-input operation (i.e. a function whose input is a vector).

• AKA: n-Ary Multivariate Function.
• Context:
  • It can range from being a Bivariate Vector Function to being a Multivariate Vector Function.
  • It can range from:
    • being a Vector-Input Value-Output Function (such as a Category-Output Function, a Vector-Input Rank-Output Function, a Vector-Input Integer-Output Function, a Vector-Input Scalar-Output Function)
    • to being a Vector-Input Tuple-Output Function, such as a Vector-Input Vector-Output Function.
• Example(s):
  • [math]\displaystyle{ f(1.1,5,3.9) \rightarrow (\pi,2.3) }[/math].
  • A Vector-Input Scalar-Output Function, such as a vector length function.
  • A Dot Product Function.
  • a Multivariate Probability Function.
  • …
• Counter-Example(s):
  • a Class Tuple-Input Function, such as [math]\displaystyle{ f(\text{Red},\text{North}) \rightarrow 4.1 }[/math]
  • a Scalar-Input Function.
  • a Set-Input Function.
  • a Vector-Output Function.
  • a Unary Function.
• See: Binary Function, Vector Relation, String Function, Vector Arity Function.

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References

2009

• (Wikipedia, 2009) ⇒ http://en.wikipedia.org/wiki/Vector_field
  • In mathematics a vector field is a construction in vector calculus which associates a vector to every point in a (locally) Euclidean space.
  • Vector fields are often used in physics to model, for example, the speed and direction of a moving fluid throughout space, or the strength and direction of some force, such as the magnetic or gravitational force, as it changes from point to point.
  • In the rigorous mathematical treatment, (tangent) vector fields are defined on manifolds as sections of a manifold's tangent bundle. They are one kind of tensor field on the manifold.

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