---
tag: 0CMHSGTWXB
kind: concept
name: Equivalent matrices
msc: [15A21]
sources:
  - url: https://en.wikipedia.org/wiki/Matrix_equivalence
    locator: lead section
same_as:
  wikidata: Q256151
  wikipedia: Matrix equivalence
---

## Summary

Two matrices of the same size are equivalent when $B = Q^{-1} A P$ for invertible matrices $P$ and $Q$; this holds exactly when they have the same rank.