Angle Bracket Left in LaTeX (\langle)

Where it is used

Opening angle bracket, used for inner products, expectation values and generated subgroups.

The left angle bracket starts notations such as the inner product \langle u, v \rangle, a bra-ket \langle \psi | \phi \rangle, the subgroup \langle g \rangle, or a time average \langle x \rangle. Never use the less-than sign < for this: it is a relation with wide spacing and the wrong shape. It works with \left and \right for automatic sizing, and with \big, \Big and friends for manual sizes. Always pair it with \rangle; if you need only one side visible, use \left. or \right. as the invisible partner.

Minimal compilable example

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

\documentclass{article}
\begin{document}
Angle Bracket Left: $\langle$

\[ \langle u, v \rangle = \sum_{i} u_i \overline{v_i} \]
\end{document}

Related symbols

• Angle Bracket Right\rangle
• Angle Brackets\langle x \rangle
• Ceiling Left\lceil
• Ceiling Right\rceil
• Ceiling\lceil x \rceil
• Floor Left\lfloor

Frequently asked questions

How do I write Angle Bracket Left in LaTeX?

Type \langle in math mode, for example $\langle u, v \rangle = \sum_{i} u_i \overline{v_i}$. It works in plain LaTeX without loading any package.

Which package do I need for \langle?

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

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

Only in math mode. Outside $...$ LaTeX stops with "Missing $ inserted", so write $\langle$ in running text. If you only need the glyph in text, paste the Unicode character ⟨ instead (with XeLaTeX or LuaLaTeX and a font that has it).