How do I horizontally align three lines inside a \left( ... \right) construction?

Question

I want to align three elements inside a pmatrix around a character that is inside a \left( ... \right) construction. Comments here have told me that the & alignment character does not work inside such a construction, which is why I get an error message reading "Misplaced &" when I attempt it.

Here's what I'm typesetting:

$$
Q_F = \begin{pmatrix}\begin{aligned}
 (1 + a) × \left(\frac{\sqrt{1}}{2} × &f(u, v) × \left(\frac{h(u)}{g(u)} - \frac{h(u)}{g(u)}\right)\right), \\
 (1 + a) × \left(\frac{\sqrt{3}}{2} × &f(u, v) × \left(\frac{h(u)}{g(u)} + \frac{h(u)}{g(u)}\right) - \frac{2 \sqrt{3} + \sqrt{6}}{6}\right), \\
-(1 + a) × \left(\frac{\sqrt{3}}{2} × &f(u, v) × \left(\frac{h(u)}{g(u)} × \frac{h(u)}{g(u)}\right) - \frac{2 \sqrt{3} - \sqrt{6}}{6} - 1\right)
\end{aligned}\end{pmatrix}
$$

And here's what I want it to look like, approximated by adding a bunch of \; space characters:

Is there a better way to line up the elements on the "f(u, v)" text instead of throwing in a bunch of extra space characters to force the issue?

Note that pure mathjax questions are off topic but you can probably formulate that as a latex question — David Carlisle, Jan 24 '24 at 14:24
align is a top level display element you can not use it inside anything else perhaps you meant to use aligned — David Carlisle, Jan 24 '24 at 14:25
@DavidCarlisle The same error message appears in a pure LaTeX environment. I've updated the question to reflect that. I also fixed the align/aligned typo in my code snippet; the problem persists when using aligned. — Lawton, Jan 24 '24 at 14:41
It would be better to completely remove the reference to mathjax and just focus on the LaTeX aspect of your question. — Teepeemm, Jan 24 '24 at 14:42
The problem is as @Teepeemm says the \left ... \right constructions. They cannot span &'s — daleif, Jan 24 '24 at 14:43
Does this answer your question? Using \left( & \right) around amsmath's align delimiter ("&"). Either use fixed size brackets, or placing the & outside the first \left will give essentially the same result. — Dai Bowen, Jan 24 '24 at 14:46
I would move the & in front of the (1+a) on each line. Then your \left...\right's are allowed. — daleif, Jan 24 '24 at 14:47

daleif · Accepted Answer · 2024-01-24T15:09:13.150

There are several issues here

align cannot be used inside display math like this (was in an earlier version of the question)
use aligned instead
you cannot use \left( ... & ... \right) that hides the & from the macros that looks for it. Move it up before (1+a)
You might get into problems with systems not understanding × in the input. I've replaced it with \times.

This works just fine in LaTeX (with amsmath loaded) and in mathjax with the proper setup:

$$
Q_F = \begin{pmatrix}\begin{aligned}
 &(1 + a) \times  \left(\frac{\sqrt{1}}{2} \times f(u, v) \times \left(\frac{h(u)}{g(u)} - \frac{h(u)}{g(u)}\right)\right), \\
 &(1 + a) \times  \left(\frac{\sqrt{3}}{2} \times f(u, v) \times \left(\frac{h(u)}{g(u)} + \frac{h(u)}{g(u)}\right) - \frac{2 \sqrt{3} + \sqrt{6}}{6}\right), \\
-&(1 + a) \times  \left(\frac{\sqrt{3}}{2} \times  f(u, v) \times \left(\frac{h(u)}{g(u)} \times \frac{h(u)}{g(u)}\right) - \frac{2 \sqrt{3} - \sqrt{6}}{6} - 1\right)
\end{aligned}\end{pmatrix}
$$

score 0 · Answer 2 · answered Jan 24 '24 at 15:20

Based on the specific material, you can take as alignment point the \times symbol.

However, without \times seems better.

\documentclass{article}
\usepackage{amsmath}
\begin{document}
\begin{equation}
Q_F =
\begin{pmatrix}
\begin{aligned}
  (1 + a) &\times \left(\frac{\sqrt{1}}{2}
           \times f(u, v)
           \times \left(\frac{h(u)}{g(u)}
           - \frac{h(u)}{g(u)}\right)\right),
\
  (1 + a) &\times \left(\frac{\sqrt{3}}{2}
           \times f(u, v)
           \times \left(\frac{h(u)}{g(u)} + \frac{h(u)}{g(u)}\right)
           - \frac{2 \sqrt{3} + \sqrt{6}}{6}\right),
\
 -(1 + a) &\times \left(\frac{\sqrt{3}}{2}
           \times f(u, v)
           \times \left(\frac{h(u)}{g(u)}
           \times \frac{h(u)}{g(u)}\right)
           - \frac{2 \sqrt{3} - \sqrt{6}}{6} - 1\right)
\end{aligned}
\end{pmatrix}
\end{equation}
\begin{equation}
Q_F =
\begin{pmatrix}
\begin{aligned}
  (1 + a) & \biggl(\frac{\sqrt{1}}{2}
            f(u, v)
            \left(\frac{h(u)}{g(u)}
           - \frac{h(u)}{g(u)}\right)\biggr),
\[\jot]
  (1 + a) & \biggl(\frac{\sqrt{3}}{2}
            f(u, v)
            \left(\frac{h(u)}{g(u)} + \frac{h(u)}{g(u)}\right)
           - \frac{2 \sqrt{3} + \sqrt{6}}{6}\biggr),
\[\jot]
 -(1 + a) & \biggl(\frac{\sqrt{3}}{2}
            f(u, v)
            \left(\frac{h(u)}{g(u)}
            \frac{h(u)}{g(u)}\right)
           - \frac{2 \sqrt{3} - \sqrt{6}}{6} - 1\biggr)
\end{aligned}
\end{pmatrix}
\end{equation}
\end{document}

How do I horizontally align three lines inside a \left( ... \right) construction?

2 Answers2