How to Write a Norm in LaTeX

Write the norm of x as \lVert x \rVert, which gives ‖x‖ with correct opening and closing spacing. \|x\| prints the same bars. Around tall content use \left\lVert … \right\rVert, and add the norm type as a subscript: \lVert x \rVert_2.

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Norm notation

\lVert x \rVert
$‖ x ‖$
Norm with left and right delimiters (amsmath); the preferred form.
\|x\|
$∥ x ∥$
Same double bar; fine for simple cases.
\left\lVert \frac{a}{b} \right\rVert
$‖ \frac{a}{b} ‖$
Bars that grow with the content.
\bigl\lVert x \bigr\rVert
$‖ x ‖$
One size larger, set by hand (also \Bigl, \biggl).
\lVert x \rVert_{\infty}
$‖ x ‖_{\infty}$
Norm type as a subscript: 1, 2, ∞, F, op.
\DeclarePairedDelimiter\norm{\lVert}{\rVert}
Text mode, no math preview
mathtools: then \norm{x}, \norm*{…} auto-sizes.

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LaTeX

Templates

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Norm examples

Each result below is drawn from the LaTeX under it. Copy the code, edit it on this page, or open it in the full editor.

Euclidean (L2) norm
$‖ x ‖_{2} = \sqrt{x_{1}^{2} + x_{2}^{2} + \dots + x_{n}^{2}}$
LaTeX
```
\lVert x \rVert_2 = \sqrt{x_1^2 + x_2^2 + \cdots + x_n^2}
```
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L1 norm
$‖ x ‖_{1} = \sum_{i = 1}^{n} | x_{i} |$
LaTeX
```
\lVert x \rVert_1 = \sum_{i=1}^{n} \lvert x_i \rvert
```
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Maximum norm
$‖ x ‖_{\infty} = max_{i} | x_{i} |$
LaTeX
```
\lVert x \rVert_{\infty} = \max_{i} \lvert x_i \rvert
```
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Triangle inequality
$‖ x + y ‖ \leq ‖ x ‖ + ‖ y ‖$
LaTeX
```
\lVert x + y \rVert \le \lVert x \rVert + \lVert y \rVert
```
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Frobenius norm
$‖ A ‖_{F} = \sqrt{\sum_{i, j} | a_{i j} |^{2}}$
LaTeX
```
\lVert A \rVert_F = \sqrt{\sum_{i,j} \lvert a_{ij} \rvert^2}
```
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Sized around a fraction
$‖ \frac{x}{‖ x ‖} ‖ = 1$
LaTeX
```
\left\lVert \frac{x}{\lVert x \rVert} \right\rVert = 1
```
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Why \lVert and \rVert

\| is one symbol used on both sides, so LaTeX cannot tell opening from closing and may space it badly after operators, for example in -\|x\|. \lVert and \rVert are marked as opening and closing delimiters, the same way \lvert and \rvert are for absolute values.

A \norm macro

In a document with many norms, define the command once with mathtools. \norm{x} gives normal-size bars, \norm*{\frac{a}{b}} grows them like \left … \right, and \norm[\big]{x} picks a size.

LaTeX

\usepackage{mathtools}
\DeclarePairedDelimiter\norm{\lVert}{\rVert}
...
$\norm{x}_2 \le \norm*{\frac{x}{2}}$

Common mistakes

Four keyboard bars are two pairs of single bars with gaps between them, not a double bar.
Instead of
```
||x||
```
Write
```
\lVert x \rVert
```
Fixed-size bars look too short next to a fraction.
Instead of
```
\| \frac{a}{b} \|
```
Write
```
\left\lVert \frac{a}{b} \right\rVert
```
\norm is not built in; define it first (MathJax and KaTeX do not have it either).
Instead of
```
\norm{x}  (no definition)
```
Write
```
\DeclarePairedDelimiter\norm{\lVert}{\rVert}
```

In Overleaf, MathJax and Word

Overleaf and pdfLaTeX
\lVert/\rVert need amsmath; \DeclarePairedDelimiter needs mathtools. \| works without packages.
MathJax and KaTeX
MathJax and KaTeX support \lVert, \rVert, \| and \left … \right. Define \norm with \newcommand if your platform allows macros.
Microsoft Word
In a Word equation type \norm then Space for ‖, or use Insert › Equation › Bracket. Copy for Word from the editor here pastes norms as editable equations.

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Norm in LaTeX: questions

How do I write a norm in LaTeX?: \lVert x \rVert, or \|x\| for quick use. Add a subscript for the norm type: \lVert x \rVert_2.
How do I make the norm bars bigger?: Use \left\lVert … \right\rVert or a fixed size such as \bigl\lVert … \bigr\rVert.
Is there a \norm command?: Not by default. Define one with mathtools: \DeclarePairedDelimiter\norm{\lVert}{\rVert}.
How is a norm different from absolute value in LaTeX?: A norm uses double bars (\lVert … \rVert), absolute value single bars (\lvert … \rvert).

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How to Write a Norm in LaTeX

Norm notation

Try it live

Norm examples

Euclidean (L2) norm

L1 norm

Maximum norm

Triangle inequality

Frobenius norm

Sized around a fraction