# Is a upright tuple a valid notation?

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 $$f\left(x\ \left|\ \begin{pmatrix} a \\ b \\ c \end{pmatrix} \right.\right)?$$

• It seems to me that you can write however you like, just so long as you make the meaning plain. – saulspatz Mar 31 at 17:28
• @saulspatz: Maybe a stupid question, but do you have any reference? I haven't seen an upright tuple anywhere so far. – Make42 Mar 31 at 17:34
• 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? – saulspatz Mar 31 at 17:39
• Do you mean '$\mathrm{argmax}$' (the point at which the maximum is attained) rather than '$\max$' (the maximum value)? – Oscar Cunningham Apr 1 at 8:11
• @OscarCunningham: Yes, I mean argmax, I'll correct it. – 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 $$(a,b,c)$$ .
• 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. – Make42 May 11 at 11:15