---
tag: 0ZCWPNZTQ3
kind: concept
name: Companion matrix
msc: [15A21]
sources:
  - url: https://en.wikipedia.org/wiki/Companion_matrix
    locator: lead section
same_as:
  wikidata: Q814361
  wikipedia: Companion matrix
---

## Summary

The companion matrix of a monic polynomial is a square matrix with ones just below the diagonal.
Its last column holds the negated coefficients, and all other entries are zero.
Its characteristic polynomial is the given polynomial.