Definition:Vector-Valued Function

Definition
Let $f_1, f_2, \cdots, f_n$ be real functions of $t$.

Let $\mathbb T \subset \R, \mathbb Y \subset \R^n$ (where usually $n \ge 2$).

Let $\mathbf r$ be a mapping from $\mathbb T \to \mathbb Y$ that maps each $t \in \mathbb T$ to a vector $\langle{f_1\left({t}\right),f_2\left({t}\right),\cdots,f_n\left({t}\right)}\rangle \in \mathbb Y$.

Then $\mathbf r$ is said to be a vector-valued function (of the parameter $t$).

If $\mathbb T$ is not explicitly defined otherwise, it is the intersection of all the domains of $f_1,f_2,\cdots,f_n$.

Component Function
Each $f_1,f_2,\cdots,f_n$ is said to be a component function of $\mathbf r$.

Also see

 * Vector-Valued Function in Terms of Standard Ordered Basis