Usually a tuple is written like $(x, y, z)$, e.g. like $$\DeclareMathOperator{\argmax}{argmax} a*, b*, c* = \argmax_{a,b,c}( \dotso\text{long line}\dotso ). $$

For my publication I don't have space for a long tuple like that in the line. So I would like to write:

$$ \begin{pmatrix} a* \\ b* \\ c* \end{pmatrix} = \argmax_{a,b,c}( \dotso\text{long line}\dotso ). $$

Is it valid notation to write a tuple upright like that?

Would it also be valid to change $$ f(x | a,b,c) $$ into $$ f\left(x\ \left|\ \begin{pmatrix} a \\ b \\ c \end{pmatrix} \right.\right)? $$

  • 1
    $\begingroup$ It seems to me that you can write however you like, just so long as you make the meaning plain. $\endgroup$ – saulspatz Mar 31 at 17:28
  • $\begingroup$ @saulspatz: Maybe a stupid question, but do you have any reference? I haven't seen an upright tuple anywhere so far. $\endgroup$ – Make42 Mar 31 at 17:34
  • $\begingroup$ No I don't have a reference, but I don't think it matters. Make a definition and use it. You've never seen an upright tuple? What about a column vector? $\endgroup$ – saulspatz Mar 31 at 17:39
  • $\begingroup$ Do you mean '$\mathrm{argmax}$' (the point at which the maximum is attained) rather than '$\max$' (the maximum value)? $\endgroup$ – Oscar Cunningham Apr 1 at 8:11
  • $\begingroup$ @OscarCunningham: Yes, I mean argmax, I'll correct it. $\endgroup$ – Make42 Apr 1 at 12:07

Traditionally, by a very useful convention, the vector $(a,b,c)$ is identified with the column matrix (or column vector) \begin{bmatrix}a\\b\\c\\ \end{bmatrix}

Unfortunately, many people nowadays think that matrices should be delineated with parentheses, not brackets. Consequently, they think that $(a,b,c)$ is a row vector (or row matrix), so they write $(a,b,c)^T$ to mean the above ordinary column vector, to avoid extravagant use of vertical space.

Since you have the opposite problem, with plenty of vertical space but restricted horizontal space, I commend to you the traditional convention, using nice straight matrix brackets, as in the display above, to denote your vector $(a,b,c)$ .

| cite | improve this answer | |
  • $\begingroup$ I see what you mean. But please note, that I do not have a vector, but a tuple, which are two very different mathematical objects. I am not sure if your observations, as useful they are for vectors, can be applied in the same way to tuples. For example, in my case, $a*$ is a real values, $b*$ is a real coordinate space vector, and $c*$ is a real matrix. $\endgroup$ – Make42 May 11 at 11:15

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.