Vector-valued function

Summary

A vector-valued function is a function whose values are vectors, for example $f \colon D \to \mathbb{R}^m$ with $D \subseteq \mathbb{R}^n$ and $m \ge 2$. Such a function has $m$ component functions $f_1, \dots, f_m \colon D \to \mathbb{R}$, with $f(x) = (f_1(x), \dots, f_m(x))$ for each $x \in D$. An example is $r(t) = (\cos t, \sin t, t)$ for $t \in \mathbb{R}$, whose values trace a helix in the Euclidean space $\mathbb{R}^3$.