How can I rotate \in by 90 degrees?

Question

I am currently trying to show the domain of variables in a simple equation:

\[\begin{matrix}
    x & \cdot & W_{1,2} & = & o\\
    \in & & \in & & \in\\
    \mdr^{1\times n} & & \mdr^{n \times m} & & \mdr^{1 \times m}
\end{matrix}\]

There are some more issues with this way to show the domain of variables, but this question is mainly about the rotated \in.

Failed tries

I've tried \usepackage{rotating}:

\[\begin{matrix}
    x & \cdot & W_{1,2} & = & o\\
    \text{\begin{rotate}{-90}$\in$\end{rotate}} & & \in & & \in\\
    \mdr^{1\times n} & & \mdr^{n \times m} & & \mdr^{1 \times m}
\end{matrix}
\]

The result looks like this:

Answer 1

The result is really ugly:

\documentclass{article}
\usepackage{graphicx,amssymb}
\newcommand{\vin}{\rotatebox[origin=c]{-90}{$\in$}}
\begin{document}
\[
\begin{array}{@{}c@{\;}c@{\;}c@{\;}c@{\;}c@{}}
x & \cdot & W_{1,2} & = & o \\
\vin && \vin && \vin \\
\mathbb{R}^{1\times n} && \mathbb{R}^{n\times m} && \mathbb{R}^{1\times m}
\end{array}
\]
\end{document}

I'd simply avoid such visual description in print; I often use something like that on the blackboard, but it's a completely different situation. I'd prefer something like

\[
x\cdot W_{1,2} = o
\]
where $x\in\mathbb{R}^{1\times n}$ and $W_{1,2}\in\mathbb{R}^{n\times m}$.

in a printed document.

Answer 2

You could try the \usepackage{rotating} package and use the \begin{rotate}{30}...\end{rotate} environment.

Or use the approach described in Rotated $\ltimes$ symbol (\rotatebox command from the graphicx package).

Answer 3

Here's an idea for annotating an equation without affecting the spacing and with a clean way of rotating the \in:

\documentclass{article}
\usepackage{amssymb}
\usepackage{tikz}
\usetikzlibrary{positioning}

\def\mdr{\mathbb{R}}

\tikzset{m/.style={inner sep=0, outer sep=0,remember picture}}
\begin{document}
\noindent
      $x_0\cdot A^n = o$
      \\[1em]
      $\tikz[m] \node (x) {$x_0$};\cdot \tikz[m] (a) \node {$A^n$}; = \tikz[m] \node (w) {$o$};$
      \begin{tikzpicture}[remember picture,overlay, node distance=.5]
        \node[shape=circle, draw=blue,minimum size=1.5em] (xc) at (x) {};
        \node[below=of x] (xd) {$\mdr^{1\times n}$};
        \path (xc) -- node[sloped] {$\in$} (xd);
      \end{tikzpicture}
\end{document}