Math & Equations

How to Define Custom Math Operators (\DeclareMathOperator)

LaTeX provides built-in operators like \sin, \cos, and \lim that are typeset in upright (Roman) font with correct spacing. When you need operators that aren't built in — like tr (trace), diag (diagonal), Var (variance), or sgn (sign) — you should declare them properly rather than typing them as italic variables. Bibby AI's template library pre-declares common operators for your field, so statistics papers come with Var, Cov, and E already defined — a head start you won't get in Overleaf.

Declare Custom Operators in the Preamble

Use \DeclareMathOperator for operators without limits (like sin, tr) and \DeclareMathOperator* for operators with limits below (like lim, argmin):

\documentclass{article}
\usepackage{amsmath}

% Without limits (subscripts stay to the side)
\DeclareMathOperator{\tr}{tr}
\DeclareMathOperator{\diag}{diag}
\DeclareMathOperator{\rank}{rank}
\DeclareMathOperator{\sgn}{sgn}

% With limits (subscripts go below in display mode)
\DeclareMathOperator*{\argmin}{arg\,min}
\DeclareMathOperator*{\argmax}{arg\,max}
\DeclareMathOperator*{\Var}{Var}

\begin{document}

$\tr(\mathbf{A}) = \sum_{i} a_{ii}$

\[
\hat{\theta} = \argmin_{\theta} \mathcal{L}(\theta)
\]

\end{document}

Inline Usage with \operatorname

For one-off operators that don't warrant a preamble declaration, use \operatorname (or \operatorname* for limits below):

% One-off operator
$\operatorname{Cov}(X, Y) = E[XY] - E[X]E[Y]$

% With limits below in display
\[
\operatorname*{ess\,sup}_{x \in \Omega} f(x)
\]

Operators with Multiple Words or Modifiers

Create operators that include subscripts, modifiers, or multi-word names:

% Probability and expectation
\DeclareMathOperator{\E}{\mathbb{E}}
\DeclareMathOperator{\Prob}{\mathbb{P}}
\DeclareMathOperator{\Cov}{Cov}

% Usage
\[
\E_{X \sim p}[f(X)] = \int f(x) \, p(x) \, dx
\]

\[
\Prob(A \mid B) = \frac{\Prob(B \mid A) \Prob(A)}{\Prob(B)}
\]

💡 Tips

•Never write $tr(A)$ or $Var(X)$ — the letters render as italic variables multiplied together, not as an operator name.
•\DeclareMathOperator provides correct spacing before and after the operator automatically.
•Place all your \DeclareMathOperator declarations together in the preamble for easy maintenance.
•Bibby AI's math-aware autocomplete suggests \DeclareMathOperator when it detects you're typing a multi-letter operator name.

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