Scalar Field Function

A Scalar Field Function is a Vector-Input Number-Output Function that is a Continuous Total Function.

• AKA: Scalar Field.
• Context:
  • It can be a Differentiable Function.
• Example(s):
  • a Gradient Function.
  • …
• Counter-Example(s):
  • a Vector Field Function.
  • a Tensor Field Function.
• See: Scalar, Field, Temperature, Pressure, Higgs Field, Scalar Field Theory.

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References

2014

• (Wikipedia, 2014) ⇒ http://en.wikipedia.org/wiki/scalar_field Retrieved:2014-9-17.
  • In mathematics and physics, a scalar field associates a scalar value to every point in a space. The scalar may either be a mathematical number or a physical quantity. Scalar fields are required to be coordinate-independent, meaning that any two observers using the same units will agree on the value of the scalar field at the same point in space (or spacetime). Examples used in physics include the temperature distribution throughout space, the pressure distribution in a fluid, and spin-zero quantum fields, such as the Higgs field. These fields are the subject of scalar field theory.

2009

• (WordNet, 2009) ⇒ http://wordnetweb.princeton.edu/perl/webwn?s=scalar%20field
  • S: (n) scalar field (a field of scalars)

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

• Eric W. Weisstein. “Scalar Function." From MathWorld -- A Wolfram Web Resource.
  • Scalar Function: A function f(x_1,...,x_n) of one or more variables whose range is one-dimensional, as compared to a vector function, whose range is three-dimensional (or, in general, n-dimensional).

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