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?
[Tex/LaTex] What’s the difference between \mathrm and \operatorname
amsmathmath-modemath-operators
Related Solutions
The star at the end of the name of a displayed math environment causes that the formula lines won't be numbered. Otherwise they would automatically get a number.
You can read about that in the amsmath user's guide since align belongs to amsmath.
Such information can usually be found in the package documentation. Type texdoc packagename at the command prompt or visit http://ctan.org/pkg/packagename. If you use google or another search engine, look for starred and commandname.
Commonly, a star symbol * means a version of a command that behaves differently from the original. That often means suppressing numbering but could also refer to special features. For example, have a look at What's the difference between \newcommand and \newcommand*?
\textrm (and the corresponding switch \rmfamily) changes an aspect of the font – in this case the family. If possible other aspects – like the series (bold or not) or the shape (italic) – are preserved. \text...-commands can be nested and their "aspect changes" are combined:
\documentclass{article}
\usepackage[T1]{fontenc}
\begin{document}
\sffamily\bfseries\itshape abc
\textrm{abc}\textrm{\textup{abc}}
\end{document}
\mathrm and the other math alphabets don't change only an aspect of a font. They switch to specific fonts. They make it possible to print symbols in special fonts. It is quite possible to setup things so that e.g. \mathrm use times, \mathbf is a bold palatino, \mathit a slanted Arial etc. You can also confuse everyone by defining \mathbf to be light itshape palatino and \mathit a bold Arial. You can define your own special math fonts e.g. \mathvector or \mathmatrix or \mathfancy. As all these commands switch to dedicated font they can't be nested. The last command (the inner one) always wins:
\documentclass{article}
\usepackage[T1]{fontenc}
\begin{document}
$\mathit{A}
\mathbf{A}
\mathit{\mathbf{A}}
\mathbf{\mathit{A}}$
\end{document}
Best Answer
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 illustrationwhere 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
\mathrmand in\operatorname. Suppose you have an operator to be called "pre-norm", with a hyphen. Here's the exampleand 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.