**Hat is a mathematical notation** used in various branches of mathematics and science. Also, the hat symbol is used in languages.

In that case, the hat symbol is usually called a **circumflex symbol.**

In latex, the hat symbol is used separately in both **text and math** modes.

Properties | Valu |
---|---|

Symbol | Hat |

Argument | Yes(a,u,i,j,k,..etc.) |

Command | `\hat{}` |

Example | `\hat{a}` → â |

## Hat symbol in math mode

LaTeX provides a default command to use the hat symbol in LaTeX’s math mode, which is `\hat{}`

.

If you pass a character as an argument to this command, the hat symbol will be printed over the character in the document.

```
\documentclass{article}
\usepackage{bm,amsmath}
% bm package for \boldsymbol command
% amsmath package for matrix
\begin{document}
$$ \hat{\mathbf{r}} = \cos(\varphi)\hat{\mathbf{i}} + \sin(\varphi)\hat{\mathbf{j}},\; \hat{\boldsymbol{\varphi}} = \hat{\mathbf{k}}\times\hat{\mathbf{r}} $$
$$ \ddot{\mathbf{r}} = \left( \ddot{r}-r\dot{\varphi}^2 \right)\hat{\mathbf{r}}+\frac{1}{r}\frac{d}{dt}\left(r^2\dot{\varphi}\right)\hat{\boldsymbol{\varphi}} $$
$$ \hat{\mathbf{i}} = \begin{pmatrix} 1 \\ 0 \\ 0 \end{pmatrix},\;\hat{\mathbf{j}} = \begin{pmatrix} 0 \\ 1 \\ 0 \end{pmatrix}, \; \hat{\mathbf{k}} = \begin{pmatrix} 0 \\ 0 \\ 1 \end{pmatrix} $$
$$ \hat{\mathbf{e}}_x\cdot(\hat{\mathbf{e}}_y\times\hat{\mathbf{e}}_z)= \varepsilon_{xyz} $$
\end{document}
```

**Output :**

If you look at the program above, you will understand that for Math mode in Latex, you have to use `$$...$$`

or `\[...\]`

on both sides of the expression.

You can easily solve the above problem using **physics** package. Because in physics, the hat symbol is used to denote the unit vector.

And you need to use `\vu`

command to define this unit vector.

```
\documentclass{article}
\usepackage{physics}
\begin{document}
$$\vu{a}$$
$$\vu*{a}$$
\end{document}
```

**Output :**

If you look at the output above, you will notice that the `*`

symbol is used with the `\vu`

command for the Greek and Italic style.

If you want to use hat symbols on more than one character, you need to use the `\widehat{}`

command instead of the `\hat{}`

command.

```
\documentclass{article}
\begin{document}
$$ \hat{abc} $$
$$ \widehat{abc} $$
\end{document}
```

**Output :**

If you look at the output above, you can see the difference between the two symbols.

## Hat symbol in text mode

This Circumflex symbol is used to write the letters of different mother tongues. For this, you need to use inline `\^{ }`

command.

```
\documentclass{article}
\begin{document}
Circumflex-\^{o},\^{a}
\end{document}
```

**Output :**

Circumflex-ô,â