Hat in LaTeX (\hat{x})

Where it is used

Places a small circumflex over one character, marking estimators, unit vectors or Fourier transforms.

Statisticians write \hat{\theta} for an estimator of \theta and \hat{y} for fitted values in regression, physicists use \hat{x} or \hat{\mathbf{n}} for unit vectors and quantum operators, and analysts write \hat{f} for the Fourier transform. The accent has a fixed width, so it only looks right over a single symbol; for several letters switch to \widehat{xy}. Over an i or j, use the dotless forms \imath and \jmath so the hat does not sit on top of a dot. In running text outside math mode the equivalent circumflex accent is \^{o}, not \hat.

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}
Hat: $\hat{x}$

\[ \hat{\beta} = (X^\top X)^{-1} X^\top y \]
\end{document}

Related symbols

• Wide Hat\widehat{xyz}
• Tilde\tilde{x}
• Wide Tilde\widetilde{xyz}
• Dot\dot{x}
• Double Dot\ddot{x}
• Triple Dot\dddot{x}

Frequently asked questions

How do I write Hat in LaTeX?

Type \hat{x} in math mode, for example $\hat{\beta} = (X^\top X)^{-1} X^\top y$. It works in plain LaTeX without loading any package.

Which package do I need for \hat{x}?

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

Can I use \hat{x} in text mode, or only in math mode?

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