If a scalar field gives out a normal number for every orders pairs what's the difference between it and a function.
[Math] Difference between Scalar field and a multivariable Function
functionsmultivariable-calculusvector-spaces
functionsmultivariable-calculusvector-spaces
If a scalar field gives out a normal number for every orders pairs what's the difference between it and a function.
Best Answer
A scalar field on $U \subseteq \mathbb{R}^n$ is a scalar-valued function $f : U \to \mathbb{R}$.
A vector field on $U \subseteq \mathbb{R}^n$ is a vector-valued function $f : U \to \mathbb{R}^n$.
These concepts appear in multivariable calculus. They are both functions, but the terminology is helpful in keeping track of what kind of objects the values of these functions are, scalars or vectors.
Added Later: It is also worth noting that sometimes you need to consider a vector-valued function which is not a vector field. Such a function on $U \subseteq \mathbb{R}^n$ is a function $f : U \to \mathbb{R}^m$ with $m \neq n$.