Tensor Product (⊗) in LaTeX

In this tutorial, I will show you how to write tensor product in LaTeX.

We can do this simply without using any external package.

The command is: \otimes, We have to write it in Mathmode.

Let’s take a look at the below example:

\documentclass{article}
\begin{document}
$A \otimes B$
\end{document}

Output:

Make the tensor product larger using \bigotimes

If you want to make the tensor product symbol larger than the previous one you can simply use \bigotimes this command.

\documentclass{article}
\begin{document}
$A \bigotimes B$
\end{document}

Output:

Put any text just below the tensor product symbol

I have created a new custom command for writing any text just below the tensor product symbol.

\documentclass{article}
\usepackage{amsmath}

\newcommand{\tens}[1]{%
  \mathbin{\mathop{\otimes}\limits_{#1}}%
}
\begin{document}
$X\tens{R}Y$
\end{document}

Output:

Text beside Tensor product in top-down position

\documentclass{article}
\usepackage{amsmath}

\newcommand{\tenside}[1]{%
  \mathbin{\mathop{\otimes}\displaylimits_{#1}}%
}
\begin{document}
$X\tenside{W}Y$
\end{document}

Output:

Another representation: subscript and superscript

\documentclass{article}
\begin{document}
$A\otimes_a^b B$
\end{document}

Output:

But it is not a better output. You have to use the \bigotimes and to make it smaller you have to redefine and scale this command. with this.

\DeclareMathOperator*{\sotimes}{\text{\raisebox{0.25ex}{\scalebox{0.6}{$\bigotimes$}}}}

\documentclass{article}
\usepackage{amsmath}
\usepackage{graphicx}
\DeclareMathOperator*{\sotimes}{\text{\raisebox{0.25ex}{\scalebox{0.6}{$\bigotimes$}}}}
\begin{document}

 $$ \bigotimes^{m}_{i=1} V_i $$
 $$ \sotimes^{m}_{i=1} V_i $$

\end{document}

Output: