Big Tensor Product in LaTeX (\bigotimes)

Where it is used

Large circled times, the tensor product of a family of spaces or operators.

Quantum computing writes the state space of n qubits as \bigotimes_{i=1}^{n} \mathbb{C}^2, and multilinear algebra builds the tensor algebra T(V) = \bigoplus_k V^{\otimes k}. The binary form \otimes joins two factors, A \otimes B, which also denotes the Kronecker product of matrices. As a large operator, \bigotimes takes stacked limits in display math. Keep the superscript form V^{\otimes n} for repeated tensor powers of one space; it is more compact than a big operator with bounds. Mention the base ring or field when it is not obvious, as in \otimes_R.

Minimal compilable example

Paste this into an empty .tex file and compile it with pdfLaTeX, XeLaTeX or LuaLaTeX.

\documentclass{article}
\usepackage{amssymb}
\begin{document}
Big Tensor Product: $\bigotimes$

\[ \mathcal{H} = \bigotimes_{i=1}^{n} \mathbb{C}^2 \]
\end{document}

Related symbols

• Big Circle Dot\bigodot
• Big Direct Sum\bigoplus
• Big Square Union\bigsqcup
• Big Vee\bigvee
• Double Sum\sum_{i=1}^{m} \sum_{j=1}^{n}
• Big Wedge\bigwedge

Frequently asked questions

How do I write Big Tensor Product in LaTeX?

Type \bigotimes in math mode, for example $\mathcal{H} = \bigotimes_{i=1}^{n} \mathbb{C}^2$. It works in plain LaTeX without loading any package.

Which package do I need for \bigotimes?

None. \bigotimes is part of standard LaTeX, so it compiles with nothing in the preamble but the document class.

Can I use \bigotimes in text mode, or only in math mode?

Only in math mode. Outside $...$ LaTeX stops with "Missing $ inserted", so write $\bigotimes$ in running text. If you only need the glyph in text, paste the Unicode character ⨂ instead (with XeLaTeX or LuaLaTeX and a font that has it).