5

I'd like to write two lines of equations, each containing two '=' symbols, in such a way that the corresponding '=' symbols will be vertically aligned.

I tried using the align environment thus:

\begin{align*}
  P^{-1}AP & = P^T\left[\lambda_1p_1, \dots, \lambda_np_n\right] & = \left[\lambda_1P^Tp_1, \dots, \lambda_nP^Tp_n\right]
  \\ & = \left[\lambda_1i_1, \dots, \lambda_ni_n\right] & = \textrm{diag}\left(\lambda_1, \dots, \lambda_n\right)
\end{align*}

But this produced this output where the second '=' symbols are not aligned. Why aren't they aligned? How can I align them?

2 Answers 2

6

The alignat* environment does it for you with two alignment characters (&) in front of the equal signs.

\documentclass[11pt]{article}
\usepackage[T1]{fontenc}
\usepackage{amsmath}

\begin{document}
  \begin{alignat*}{2}
    P^{-1}AP & = P^T\left[\lambda_1p_1, \dots, \lambda_np_n\right] && = \left[\lambda_1P^Tp_1, \dots, \lambda_nP^Tp_n\right] \\
    & = \left[\lambda_1i_1, \dots, \lambda_ni_n\right] && = \textrm{diag}\left(\lambda_1, \dots, \lambda_n\right)
  \end{alignat*}
\end{document}

Further reading


enter image description here


Addendum

For comparison without automatically scaled delimiters and "diag" as operator.

\documentclass[11pt]{article}
\usepackage[T1]{fontenc}
\usepackage{amsmath}

\DeclareMathOperator*{\diag}{diag}

\begin{document}
  \begin{alignat*}{2}
    P^{-1}AP &= P^T [\lambda_1p_1, \dots, \lambda_np_n] &&= [\lambda_1P^Tp_1, \dots, \lambda_nP^Tp_n] \\
    &= [\lambda_1i_1, \dots, \lambda_ni_n] &&= \diag(\lambda_1, \dots, \lambda_n)
  \end{alignat*}
\end{document}

enter image description here

7
  • 2
    It would be better if you removed the useless \left and \right and turned \textrm{diag} into \operatorname{diag}.
    – egreg
    Mar 4, 2014 at 9:08
  • @egreg: These are not my idea and just copied from the question. And by the way, they can also be found in the other answer. The same applies to "diag". Your comment would be more appropriate to the question. Mar 4, 2014 at 9:11
  • @egreg: Why are the \left and \right useless? Do they have any cons? What would be a suitable circumstance to use them?
    – Evan Aad
    Mar 4, 2014 at 9:19
  • @EvanAad They just add unwanted space, and slightly increase the size in the part above “diag”, which unbalances the display.
    – egreg
    Mar 4, 2014 at 9:21
  • 1
    @EvanAad then use mleftright package (see documentation).
    – Manuel
    Mar 4, 2014 at 10:31
5

You need two &. The first of the two is for the left part (here empty) of the second equation system:

\documentclass{article}
\usepackage{amsmath}
\begin{document}
\begin{align*}
  P^{-1}AP & = P^T\left[\lambda_1p_1, \dots, \lambda_np_n\right] && =
 \left[\lambda_1P^Tp_1, \dots, \lambda_nP^Tp_n\right]
  \\
  & = \left[\lambda_1i_1, \dots, \lambda_ni_n\right] && =
 \textrm{diag}\left(\lambda_1, \dots, \lambda_n\right)
\end{align*}
\end{document}

Result

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