2

Is it convention to bold any function with more than one output?

For example, $\textbf{f}:\textbf{R}^2 \mapsto \textbf{R}^3$ or $f: \textbf{R}^2 \mapsto \textbf{R}^3$

$\textbf{f}(\textbf{x})$ or $f(\textbf{x})$

Fgilan
  • 393
  • 2
    Not where I'm from. But some people like to bold vectors, so perhaps that crowd would bold vector valued functions. – jgon Oct 01 '15 at 21:02
  • 1
    Also, your $\mathbf f$ has only one output for each input, which happens to be an element of $\mathbb R^3$ – Hagen von Eitzen Oct 01 '15 at 21:04
  • 1
    In some settings it is useful to write vectors in bold. Then it would be common to write vector-valued functions also in bold. In other settings this is not common. So: follow the conventions of the area. – GEdgar Oct 01 '15 at 21:06
  • In physics the bold face notation is quite common. – Urgje Oct 01 '15 at 22:16

1 Answers1

3

There are various different conventions, and it varies depending on field and location: in some countries, people write rot for the curl of a vector field, for example. And it also depends on whether handwriting or typing (I've yet to see someone use convincing boldface in normal handwritten working!)

In particular, the following can all mean a vector with symbol $v$, depending on definitions: $$ v \quad \mathbf{v} \quad \underline{v}, \quad \vec{v}, \quad v_i, \quad v^i $$ (regarding the last ones, yes, I am aware that it's a misunderstanding of vectors v. their components, but physicists and applied mathematicians use it (and it does save writing out $v^i \mathbf{e}_i$ all the time).

All of these conventions may or may not also apply to functions. In addition, you have $$ \nabla, \quad \pmb{ \nabla}, \quad \vec{\nabla}, \quad \underline{\nabla}, $$ all the same differential operator. (And don't get me started on conventions for the Laplacian and the Fourier transform...)

Chappers
  • 67,606