How to write norm symbol in LaTeX like ||a||?

There are many ways to represent the norm symbol in a latex document. However, in all cases, the shape of this symbol does not increase or decrease dynamically.

So, in this tutorial, we will discuss the best method which will be the best practice for you.

Symbol Norm symbol
Type Mathematics
Package Default, physics, mathtools
Commands \|..\|, \lVert..\rVert, \Vert
Example \lVert  x  \rVert → ⌊x⌋

Most of the time you will use the double bar on both sides of the expression or variable to represent the norm symbol that is on your keyboard.

\documentclass{article}
\begin{document}
  $$ || x || $$
  $$ || x^{2} || $$
  $$ || \frac{x}{y} || $$
\end{document}

Output :

use double bar for norm symbol

You can use a backslash single bar instead of a double bar, which will return you the same output. For example

\documentclass{article}
\begin{document}
  $$ \| x \| $$
  $$ \| y \| $$
  $$ \| \frac{x}{y} \| $$
\end{document}

Output :

use backslash single bar for norm symbol

You can use \lVert and \rVert or \Vert commands for double bar symbols. However, for each command, the letter V will be capitalized. Because latex is case-sensitive.

\documentclass{article}
\usepackage{physics}
\begin{document}
  $$ \Vert x \Vert $$
% -- Use physics package for \lVert and \rVert commands -- 
  $$ \lVert y \rVert $$
  $$ \lVert \frac{x}{y} \rVert $$
\end{document}

Output :

use \lVert and \rVert or \Vert commands

When you use this symbol multiple times in a document, it may not feel good to write such a large syntax over and over again. So, in this case, the big syntax is converted into a small command with the help of \newcommand.

\documentclass{article}
\usepackage{amsmath}
\newcommand\norm[1]{\lVert#1\rVert}
\newcommand\normx[1]{\Vert#1\Vert}
\begin{document}
 $$ \norm{x }$$
 $$ \normx{y} $$
 $$ \normx{\frac{x}{y}} $$
\end{document}

Output :

big syntax is converted into a small command with the help of \newcommand.

Big or responsive size norm symbol

In all the commands discussed above for the norm symbol, the shape of the symbol does not increase and decrease dynamically according to the shape of the expression.

\documentclass{article}
\usepackage{amsmath}
\newcommand\norm[1]{\lVert#1\rVert}
\newcommand\normx[1]{\Vert#1\Vert}
\begin{document}
  $$ \norm{\frac{x}{y}} $$
  $$ \norm{\sum_{i=1}^{n}x_{i}} $$
  $$ \normx{\frac{w}{v}} $$
  $$ \normx{w} $$
\end{document}

Output :

norm symbol

However, for this responsive size norm symbol, you need to use the \left and \right commands before the present command. for example

\documentclass{article}
\usepackage{amsmath}
\newcommand\norm[1]{\left\lVert#1\right\rVert}
\newcommand\normx[1]{\left\Vert#1\right\Vert}
\begin{document}
 $$ \norm{\frac{x}{y}} $$ 
 $$ \norm{\sum_{i=1}^{n}x_{i}} $$ 
 $$ \normx{\frac{w}{v}} $$ 
 $$ \normx{w} $$
\end{document}

Output :

Big or responsive size norm symbol.

Use physics package for norm symbol in LaTeX

The physics package contains the predefine \norm command for this symbol. And this command will return you the norm symbol of responsive size.

\documentclass{article}
\usepackage{physics}
\begin{document}
 $$ \norm{\frac{x}{y}} $$ 
 $$ \norm{A_{i,j}} $$
 $$ \norm{\frac{w}{v}} $$
 $$ \norm{\sum_{i=1}^{n}\frac{x_i}{\abs{x}}} $$
\end{document}

Output :

In physics package, use \norm command for norm symbol.

Second, you can use four types of big commands for different sizes with the norm command.

\documentclass{article}
\usepackage{physics}
\begin{document}
 $$ \norm\big{\frac{v}{w}} \; \norm\Big{\frac{v}{w}} \; \norm\bigg{\frac{v}{w}} \; \norm\Bigg{\frac{v}{w}} $$ 
\end{document}

Output :

use four types big commands with \norm.

And if you want a norm symbol of constant size, use the * sign with the command like \norm*.

\documentclass{article}
\usepackage{physics}
\begin{document}
 $$ \norm*{w} $$
 $$ \norm*{\frac{v}{w}} $$
 $$ \norm*{V_{i,j}} $$
 $$ \norm*{\sum_{i=1}^{n}x_{i}} $$
\end{document}

Output :

norm symbol of constant size.

Use mathtools package for norm symbol in LaTeX

There are no predefined commands in mathtools packages like physics package for this symbol, you can define new commands with the help of \DeclarePairedDelimiter.

\documentclass{article}
\usepackage{mathtools}
\DeclarePairedDelimiter\norm{\lVert}{\rVert}
\begin{document}
 $$ \norm{w} $$
 $$ \norm{\frac{v}{w}} $$
 $$ \norm{\sum_{i=1}^{n}(x_{i})^2} $$
 $$ \sum_{i=1}^{n}\frac{w}{\norm{w_i}} $$
\end{document}

Output :

Use mathtools package for norm symbol.

You notice the output above, the size of the norm symbol is not adjusting with the size of the expression. For this, you need to use the star symbol along with the norm command.

\documentclass{article}
\usepackage{mathtools}
\DeclarePairedDelimiter\norm{\lVert}{\rVert}
\begin{document}
 $$ \norm*{w} $$
 $$ \norm*{\frac{v}{w}} $$
 $$ \norm*{\sum_{i=1}^{n}(x_{i})^2} $$
 $$ \sum_{i=1}^{n}\frac{w}{\norm*{w_i}} $$
\end{document}

Output :

Use the star symbol along with the norm command.

And you can use four types of big commands like \big, \Big, \bigg, and \Bigg as optional arguments with this command. Which returns you a variety of sizes. For example

\documentclass{article}
\usepackage{mathtools}
\DeclarePairedDelimiter\norm{\lVert}{\rVert}
\begin{document}
 $$ \norm[\big]{\frac{x}{y}} \; \norm[\Big]{\frac{x}{y}} \; \norm[\bigg]{\frac{x}{y}} \; \norm[\Bigg]{\frac{x}{y}} $$
\end{document}

Output :

Use four types of big commands like \big, \Big, \bigg, and \Bigg as optional arguments with this command.

Norm of vector in LaTeX

You will notice that the norm symbol is used with the vector. For example

\documentclass{article}
\usepackage{physics,amsmath}
\begin{document}
 $$ \norm{k\vec{a}}=\abs{k}\norm{\vec{a}} $$
 $$ \vu*{a}=\frac{\vec{a}}{\norm{\vec{a}}} $$
 $$ \norm{\vec{u}} = \sqrt{u^2_1 + u^2_2 + \cdots + u^2_n} $$
\end{document}

Output :

Norm of vector.

In latex, the best practice is to use the physics package for the norm symbol. Because there are predefined commands in the physics package, you don’t need to write large syntax separately.

And there are a lot of examples in this tutorial to help you understand. I hope you have found the answer to your question.

One request!

Don't forget to share this tutorial if I have added any value to your education life with this tutorial.

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