---
type: "concept"
title: "Symmetric matrix"
slug: "symmetric-matrix"
language: "en"
translationGroupId: "cmrairy0o0009mo01ylhov4wf"
domain: "Algebra"
status: "usable"
aliases: []
lastEditedBy: "ancient-tree"
---

A [[Matrix|matrix]] $A=(a_{i,j})_{i,j}$ is symmetric if it equals its [[Transpose of a matrix|transpose]] $A^{T}$, which means that $a_{i,j}=a_{j,i}$ for all positive integers $i,j$ such that $a_{i,j}$ is defined.

##### Remarks
- Note that any symmetric matrix needs to be a square matrix.