How to set \phantom{-} automatically for entries of matrices?

Question

I want a way to set matrix entries aligned by their sign automatically. For example, output of

\begin{bmatrix}
    1&1&-1\\
    -1&1& 1\\
    1&-1& 1
\end{bmatrix}

be same as output of

\begin{bmatrix}
    \phantom{-}1&\phantom{-}1&-1\\
    -1&\phantom{-}1& \phantom{-}1\\
    \phantom{-}1&-1& \phantom{-}1
\end{bmatrix}

Is it possible at all?

Answer 1

The amsmath environments [pbBvV]?matrix use a common \env@matrix macro to start the alignment. In this macro there is \array{*\c@MaxMatrixCols c}, which centers the contents of the cells by default. One quick way to change that default globally is to redefine that macro with r instead of c, or load etoolbox and do \patchcmd\env@matrix{c}{r}{}{}.

Alternatively, you can redefine \env@matrix to take an argument for the alignment, and patch the environments which use it to check for such optional argument. This is essentially what mathtools's starred environments do.

In the code below I used a loop to patch all the environments in one go (with a single default), but you can change them selectively if you want different behaviours.

Also, if you use a right aligned cell, then the numbers will be right aligned (thanks, Sherlock), and if two numbers have different widths (say, -1 and -12), then their rightmost end will be aligned, not the minus signs. To align the minus sign you can use the J column type defined (and not defined) in Schrödinger's cat's answer.

\documentclass{article}
\usepackage{amsmath}
\usepackage{array}
\usepackage{etoolbox}
\makeatletter
\def\env@matrix[#1]{\hskip -\arraycolsep
  \let\@ifnextchar\new@ifnextchar
  \array{*\c@MaxMatrixCols #1}}
\@tfor\@temp:=\matrix\pmatrix\bmatrix\Bmatrix\vmatrix\Vmatrix\do
  {\expandafter\patchcmd\@temp
     {\env@matrix}
     {\@ifnextchar[%]   default V
        \env@matrix{\env@matrix[J]}}
     {}{\FAILED}}
% From Mr. Cat's answer: https://tex.stackexchange.com/a/522747/134574
\newcolumntype{J}{>{\CheckSign}l}
\def\CheckSign\ignorespaces{%
  \@ifnextchar-{}{\@ifnextchar+{}{\phantom{-}}}}
\makeatother
\begin{document}
\[
\begin{bmatrix}
    1&1&-1\\
    -1&1& 1\\
    1&-1&-12\\
    1&-1&+12
\end{bmatrix}
\]
\end{document}

Answer 2

Here are two more proposals. The first one is conceptually very similar to Sebastiano's nice answer (and can be seen as an addendum to his). One can set the column type to r also with the mathtools package. The second proposal is based on this very nice answer, which solves a very related problem. It really does what you ask for, i.e. inserts a \phantom{-} if there is no minus, and comes in two variations, one with c and one with l columns (which I think makes more sense).

\documentclass{article}
\usepackage{mathtools}
\usepackage{array}% for second solution 
\makeatletter
\def\CheckMinus\ignorespaces{\@ifnextchar-{}{\phantom{-}}}
\makeatother
\newcolumntype{I}{>{\CheckMinus}c}
\newcolumntype{J}{>{\CheckMinus}l}

\begin{document}
\begin{enumerate}
 \item Just mathtools and change column type to \texttt{r}.
\[
\begin{bmatrix*}[r]
    1&1&-1\\
    -1&1& 1\\
    1&-1& 1
\end{bmatrix*}\quad\text{and}\quad\begin{bmatrix*}[r]
    12&1&-12\\
    -1&1& 12\\
    1&-12& 1
\end{bmatrix*}
\]
 \item Insert \verb|\phantom{-}| if there is no minus and use \texttt{c} column.
\[
\begin{bmatrix*}[I]
    1&1&-1\\
    -1&1& 1\\
    1&-1& 1
\end{bmatrix*}\quad\text{and}\quad\begin{bmatrix*}[I]
    12&1&-12\\
    -1&1& 12\\
    1&-12& 1
\end{bmatrix*}
\]
 \item Insert \verb|\phantom{-}| if there is no minus and use \texttt{l} column.
\[
\begin{bmatrix*}[J]
    1&1&-1\\
    -1&1& 1\\
    1&-1& 1
\end{bmatrix*}\quad\text{and}\quad\begin{bmatrix*}[J]
    12&1&-12\\
    -1&1& 12\\
    1&-12& 1
\end{bmatrix*}
\]
\end{enumerate}
\end{document}

Answer 3

You can use the spalign package. Here there is an example for your request.

%% Compile and read me!
\documentclass[a4paper,12pt]{article}
\usepackage{spalign}
\begin{document}
\[ \spalignmat[r]{-1 1 -1; -1 1 1; 1 -1 1} \]
\end{document}