Long dashes for denoting omitted columns of a matrix

Question

Mathematicians would often to like to think of a row of a m by n matrix with entries from a , say, field, as a vector in the n-dimensional vector space over the field.

Though I am not a mathematician yet, I am stuck with a situation where my proof becomes significantly simpler if I did not care about the entries of the row but just think of it as a vector.

For instance, I'd like my rows to look like how the columns look here. The code for one of the matrices there:

$P=
\begin{bmatrix} 
\biggl |& \biggl|&\biggl|\\
x_1&x_2 &x_3\\
\biggl|&\biggl|&\biggl|
\end{bmatrix}$

I'd be grateful if some one helped me.

Answer 1

Here's a way, inspired by \rightarrofill:

\documentclass{article}
\usepackage{amsmath}

\makeatletter
\newcommand{\longdash}[1][2em]{%
  \makebox[#1]{$\m@th\smash-\mkern-7mu\cleaders\hbox{$\mkern-2mu\smash-\mkern-2mu$}\hfill\mkern-7mu\smash-$}}
\makeatother
\newcommand{\omitskip}{\kern-\arraycolsep}
\newcommand{\llongdash}[1][2em]{\longdash[#1]\omitskip}
\newcommand{\rlongdash}[1][2em]{\omitskip\longdash[#1]}

\begin{document}
\[
\begin{bmatrix}
\llongdash & x_{1}   & \rlongdash \\
\llongdash & x_{2}+y & \rlongdash \\
\llongdash & x_{n}   & \rlongdash
\end{bmatrix}
\]
\end{document}

I use \llongdash and \rlongdash to back up slightly and so to ensure the correct alignment of the dashes.

If dots are needed for denoting omitted rows, one can use \hdotsfor:

\begin{bmatrix}
\llongdash & x_{1}   & \rlongdash \\
\llongdash & x_{2}+y & \rlongdash \\
\hdotsfor{3} \\
\llongdash & x_{n}   & \rlongdash
\end{bmatrix}

instead of the code above will produce

Alternatively, one can use only one column

\[
\begin{bmatrix}
\longdash\hfill x_{1} \hfill \longdash \\
\longdash\hfill x_{2} + y \hfill \longdash \\
\longdash\hfill x_{n} \hfill \longdash \\
\end{bmatrix}
\]

and get

Answer 2

Here is a solution based on TikZ:

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{matrix}

% possible to customize here the dash aspect
\newcommand{\mydash}{
\draw(0.3,0.5ex)--(-0.3,0.5ex);
}

\begin{document}
\[P=
\begin{tikzpicture}[baseline=-0.5ex]
\matrix(m)[matrix of math nodes,left delimiter=(,right delimiter=),ampersand replacement=\&]
{
\mydash \&   y_1 \&   \mydash   \\
\mydash \&   y_2+z_2 \&  \mydash    \\
\mydash \&   y_3 \&   \mydash \\
};
\end{tikzpicture}
\]

\end{document}

which gives: