# How to Space Displayed Mathematical Equations

In a displayed mathematical equation with more than one component, how much space should be placed between the components?

Here are the guidelines I use, with examples in LaTeX. Recall that a \quad is approximately the width of a capital M and \qquad is twice the width of a \quad.

## Case 1. Equation with Qualifying Expression

An equation or other mathematical construct is separated from a qualifying expression by a \quad. Examples:

$\notag |a_{ii}| \ge \displaystyle\sum_{j\ne i} |a_{ij}|, \quad i=1\colon n.$

$\notag fl(x\mathbin{\mathrm{op}}y) = (x\mathbin{\mathrm{op}} y)(1+\delta), \quad |\delta|\le u, \quad \mathbin{\mathrm{op}} =+,-,*,/.$

$\notag y' = t^2+y^2, \quad 0\le t\le 1, \quad y(0)=0.$

When the qualifying expression is a prepositional phrase it is given standard sentence spacing. Examples:

$\notag \min_x c^Tx \quad \mathrm{subject~to~} Ax=b,~ x\ge 0.$

$\notag \|J(v)-J(w)\| \le \theta_L \|v-w\| \quad \mathrm{for~all~} v,w \in \mathbb{R}^n.$

The first example was typed as (using the equation* environment provided by the amsmath package)

\begin{equation*}
\min_x c^Tx \quad \text{subject to $Ax=b$, $x\ge 0$}.
\end{equation*}


Here, the qualifying phrase is placed inside a \text command, which jumps out of math mode and formats its argument as regular text, with the usual interword spacing in effect, and we re-enter math mode for the conditions. This is better than writing

\min_x c^Tx \quad \text{subject to} ~Ax=b, ~x\ge 0.


with hard spaces. Note that \text is a command from the amsmath package, and it is similar to the LaTeX command \mbox and the TeX command \hbox, both of which work equally well here.

## Case 2. Equation with Conjunction

When an equation contains a conjunction such as and or or, the conjunction has a \quad on each side. Examples:

$\notag x = 1 \quad \mathrm{or} \quad x = 2.$

$\notag a = \displaystyle\sum_{j=1}^n c_j v_j \quad \mathrm{where} \quad c_j = \langle a,~ u_j\rangle~\mathrm{for}~j=1,2,\dots,n.$

In the second example, one might argue for a \quad before the qualifying “for”, on the basis of case 1, but it I prefer the word spacing. This example was typed as

\begin{equation*}
\text{$c_j = \langle a, u_j\rangle$ for $j=1,2,\dots,n$}.
\end{equation*}


## Case 3. Multiple Equations

Two or more equations are separated by a \qquad. Examples:

$\notag A = e_1^{}e_3^T, \qquad B = e_1^{}e_4^T, \qquad C = e_2^{}e_3^T, \qquad D = e_2^{}e_4^T$

\notag \begin{aligned} AXA &= A, \qquad & XAX &= X,\\ (AX)^* &= AX, \qquad & (XA)^* &= XA. \end{aligned}

## Limitations

It is important to emphasize that one might diverge from following these (or any other) guidelines, for a variety of reasons. With a complicated display, or if a narrow text width is in use (as with a two-column format), horizontal space may be at a premium so one may need to reduce the spacing. And the guidelines do not cover every possible situation.

## Notes

My guidelines are the same ones that were used in typesetting the Princeton Companion to Applied Mathematics, and I am grateful to Sam Clark (T&T Productions), copy editor and typesetter of the Companion, for discussions about them. Cases 1 and 3 are recommended in my Handbook of Writing for the Mathematical Sciences (2017).

The SIAM Style Guide (link to PDF) prefers a \qquad in Case 1 and \quad in Case 3 with three or more equations. The AMS Style Guide (link to PDF) has the same guidelines as SIAM. Both SIAM and the AMS allow an author to use just a \quad between an equation an a qualifying expression.

In the TeXbook (1986, p. 166), Knuth advocates using a \qquad between an equation and a qualifying expression.