[Tex/LaTex] How to rotate \in by 90 degrees

rotatingsymbols

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

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

enter image description here

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:

enter image description here

Best Answer

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}

enter image description here

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.

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