---
tag: 0MKRHZB3WS
kind: concept
name: Change of basis matrix
aliases: [transition-matrix]
msc: [15A03, 15A04]
sources:
  - url: https://en.wikipedia.org/wiki/Change_of_basis
    locator: Change-of-basis formula
---

## Summary

The change of basis matrix from one basis to another is a square matrix.
Its columns are the coordinate vectors of the new basis vectors in the old basis.
It converts new coordinates into old coordinates.