# [Tex/LaTex] What’s the difference between \mathrm and \operatorname

amsmathmath-modemath-operators

I apparently can't see the difference in a compilation (pdflatex) between \mathrm and \operatorname. So, as in the title the question is: is there a difference? Which one is preferable in what occasions?

There are many differences. The main one is in the fact that \mathrm{xyz} behaves like an ordinary letter, while \operatorname{xyz} behaves like function names such as \sin. Here's an illustration

$\sin x + \sin(x+y) + a\sin z$

$\mathrm{sin} x + \mathrm{sin}(x+y) + a\mathrm{sin}z$


where it's clear that the second line is typeset wrong. Even if your "operator" requires parentheses after it, it should be \operatorname, as the third summand shows, where a thin space separates the coefficient from the operator.

Another subtle difference is in how some characters are interpreted in \mathrm and in \operatorname. Suppose you have an operator to be called "pre-norm", with a hyphen. Here's the example

$\operatorname{pre-norm}(\mathbf{v})$

$\mathrm{pre-norm}(\mathbf{v})$


and now it's clear what is to be used. Indeed \operatorname (and the same holds for macros defined with \DeclareMathOperator) treats punctuation symbols in a special way; \mathrm, instead, treats them as math symbols.