---
tag: 08SP3DF8NB
kind: concept
name: Permutation matrix
msc: [15A99, 05A05]
sources:
  - url: https://en.wikipedia.org/wiki/Permutation_matrix
    locator: lead section
same_as:
  wikidata: Q851512
  wikipedia: Permutation matrix
---

## Summary

A permutation matrix is a square matrix with exactly one entry $1$ in each row and each column, and all other entries $0$.
It permutes the coordinates of a vector.