Perpendicular in LaTeX (\perp)

Where it is used

Perpendicular relation, marking orthogonal lines, vectors or subspaces, and independence of variables.

Geometry writes AB \perp CD, linear algebra writes u \perp v when \langle u, v \rangle = 0 and W^\perp for an orthogonal complement, and number theory sometimes uses a \perp b for coprime integers. Probabilists write X \perp Y for independence, often doubled as X \perp\!\!\!\perp Y to imitate the dedicated independence symbol. \perp is a relation with spacing on both sides, whereas \bot has the same shape but ordinary spacing, which suits the logical falsum or a bottom element. In a superscript like W^\perp either works, since spacing is suppressed there.

Also listed under: Probability & Statistics, Geometry, Number Theory

Minimal compilable example

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

\documentclass{article}
\begin{document}
Perpendicular: $\perp$

\[ W^{\perp} = \{ v \in V : v \perp w \ \forall w \in W \} \]
\end{document}

Related symbols

• Parallel\parallel
• Superset or Equal\supseteq
• Not Parallel\nparallel
• Superset\supset
• Much Less Than\ll
• Proper Subset\subsetneq

Frequently asked questions

How do I write Perpendicular in LaTeX?

Type \perp in math mode, for example $W^{\perp} = \{ v \in V : v \perp w \ \forall w \in W \}$. It works in plain LaTeX without loading any package.

Which package do I need for \perp?

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

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

Only in math mode. Outside $...$ LaTeX stops with "Missing $ inserted", so write $\perp$ 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).