Big Direct Sum in LaTeX (\bigoplus)

Where it is used

Large circled plus, the direct sum of a family of spaces or modules.

A diagonalizable operator splits its space into eigenspaces, V = \bigoplus_{\lambda} E_\lambda, and graded rings appear as \bigoplus_{n \ge 0} R_n. \oplus is the binary form for two summands, U \oplus W. In computer science and cryptography, \bigoplus_{i} x_i often means the XOR of many bits, reusing the same glyph. Limits stack in display style like \sum. Note that the direct sum of infinitely many modules differs from the direct product \prod, which allows infinitely many nonzero components, so choose the operator that matches your construction.

Minimal compilable example

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

\documentclass{article}
\begin{document}
Big Direct Sum: $\bigoplus$

\[ V = \bigoplus_{i=1}^{k} \ker(A - \lambda_i I) \]
\end{document}

Related symbols

• Big Tensor Product\bigotimes
• Big Vee\bigvee
• Big Circle Dot\bigodot
• Big Wedge\bigwedge
• Big Square Union\bigsqcup
• Big Intersection with Index\bigcap_{i=1}^{n}

Frequently asked questions

How do I write Big Direct Sum in LaTeX?

Type \bigoplus in math mode, for example $V = \bigoplus_{i=1}^{k} \ker(A - \lambda_i I)$. It works in plain LaTeX without loading any package.

Which package do I need for \bigoplus?

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

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

Only in math mode. Outside $...$ LaTeX stops with "Missing $ inserted", so write $\bigoplus$ 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).