---
tag: 0E89HQATM8
kind: concept
name: Similar matrices
aliases: [conjugate-matrices]
msc: [15A21]
sources:
  - url: https://en.wikipedia.org/wiki/Matrix_similarity
    locator: lead section
same_as:
  wikidata: Q254491
  wikipedia: Matrix similarity
---

## Summary

Two square matrices are similar when they are the matrices of the same endomorphism in two bases.
Equivalently, $B = P^{-1} A P$ for an invertible matrix $P$.