Vector-Input Scalar-Output Function

A Vector-Input Scalar-Output Function is a vector input function that is a scalar-output function.

• AKA: Real-Valued Vector Function, Multi-Dimensional Scalar Function.
• Context:
  • It can range from being a Vector-Input Scalar-Output Algebraic Function to being a Vector-Input Scalar-Output Black-Box Function.
• Context:
  • It can be a Differentiable Function.
  • It can have a Partial Derivative on one of its Dimensions.
• Example(s):
  • [math]\displaystyle{ f }[/math](1.1,2.3,3.9) ⇒ 3.2
  • [math]\displaystyle{ f }[/math](1.5) ⇒ 3.1
  • a Vector-Input Polynomial Function of [math]\displaystyle{ f(x,y) = \frac{1}{3} y^2 − 2.3 x + 6 }[/math].
  • …
• Counter-Example(s):
  • a Set-Input Real Number-Output Function.
  • a Tuple-Input Scalar-Output Function.
  • a Vector-Input Categorical-Output Function.
• See: Number-Input Function.

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References

2009

• http://en.wiktionary.org/wiki/scalar_function
  • • 1. (mathematics) Any function whose domain is a vector space and whose value is its scalar field

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