Double Sum in LaTeX (\sum_{i=1}^{m} \sum_{j=1}^{n})

Where it is used

Two nested sums, over i from 1 to m and j from 1 to n, as when adding a matrix's entries.

Double sums add up every entry of an m by n array, as in the Frobenius norm \lVert A \rVert_F^2 = \sum_{i=1}^{m} \sum_{j=1}^{n} a_{ij}^2. LaTeX places the two operators side by side with suitable spacing, so no manual space is needed between them. When both indices share a condition, a single sign such as \sum_{i,j} or \sum_{1 \le i < j \le n} is more compact, and \substack stacks several conditions under one sigma. Swapping the order of finite double sums is always valid, but infinite ones need absolute convergence or nonnegative terms.

Minimal compilable example

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

\documentclass{article}
\usepackage{amsmath}
\begin{document}
Double Sum: $\sum_{i=1}^{m} \sum_{j=1}^{n}$

\[ \lVert A \rVert_F^2 = \sum_{i=1}^{m} \sum_{j=1}^{n} a_{ij}^2 \]
\end{document}

Related symbols

• Indexed Sum\sum_{k \in K}
• Big Square Union\bigsqcup
• Big Circle Dot\bigodot
• Big Tensor Product\bigotimes
• Big Direct Sum\bigoplus
• Big Vee\bigvee

Frequently asked questions

How do I write Double Sum in LaTeX?

Type \sum_{i=1}^{m} \sum_{j=1}^{n} in math mode, for example $\lVert A \rVert_F^2 = \sum_{i=1}^{m} \sum_{j=1}^{n} a_{ij}^2$. It works in plain LaTeX without loading any package.

Which package do I need for \sum_{i=1}^{m} \sum_{j=1}^{n}?

None. \sum_{i=1}^{m} \sum_{j=1}^{n} is part of standard LaTeX, so it compiles with nothing in the preamble but the document class.

Can I use \sum_{i=1}^{m} \sum_{j=1}^{n} in text mode, or only in math mode?

Only in math mode. Outside $...$ LaTeX stops with "Missing $ inserted", so write $\sum_{i=1}^{m} \sum_{j=1}^{n}$ in running text.