Norm in LaTeX (\| x \|)

Where it is used

Encloses a vector or function in double bars to denote its norm, its length or size.

Norms are everywhere in analysis and linear algebra: the Euclidean norm \|x\|_2, the sup norm \|f\|_\infty, the Frobenius norm \|A\|_F, and the triangle inequality \|x + y\| \le \|x\| + \|y\|. A subscript after the closing bar indicates which norm. Writing \lVert x \rVert instead of \| x \| gives better spacing in expressions like \|{-x}\|, since LaTeX then knows each bar's role. For tall content, such as fractions inside the norm, use \left\| ... \right\|. Single bars |x| are reserved for absolute values.

Also listed under: Linear Algebra

Minimal compilable example

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

\documentclass{article}
\begin{document}
Norm: $\| x \|$

\[ \|x + y\| \le \|x\| + \|y\| \]
\end{document}

Related symbols

• Double Bracket Left\llbracket
• Double Vertical Bar\|
• Double Bracket Right\rrbracket
• Floor\lfloor x \rfloor
• Double Brackets\llbracket x \rrbracket
• Floor Right\rfloor

Frequently asked questions

How do I write Norm in LaTeX?

Type \| x \| in math mode, for example $\|x + y\| \le \|x\| + \|y\|$. It works in plain LaTeX without loading any package.

Which package do I need for \| x \|?

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

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

Only in math mode. Outside $...$ LaTeX stops with "Missing $ inserted", so write $\| x \|$ in running text.