Vector as argument of a function

Question

Given a function $f(x)=y$ is correct to say that $f\left(\left[\begin{array}{c} x_1 \\ x_2 \\ x_3 \end{array}\right]\right)=\left[\begin{array}{c} y_1 \\ y_2 \\ y_3 \end{array}\right]$?

Answer 1

Yes, assuming that $x \in A^3$ and $y \in B^3$ for some suitable spaces $A,B$ you just give the explicit representation of those elements which is equivalent to actually writing $x$ or $y$.

If you want to make it even more formal you can say for example that the $x_i$ represent the coordinate entries of $x$, but that is common notation anyways and most people will understand it.