---
type: "concept"
title: "Orthogonal matrix"
slug: "orthogonal-matrix"
language: "en"
translationGroupId: "cmrced6c3000fs701xl4tghb8"
domain: "Algebra"
status: "usable"
aliases: []
lastEditedBy: "ancient-tree"
---

An orthogonal matrix is a real [[Square matrix|square matrix]] $A\in M_{n}(\R)$ satisfying
$$A\,A^{T}=A^{T}\,A=I_{n}$$
where $A^{T}$ is the [[Transpose of a matrix|transpose]] of $A$.