---
tag: 0YQSGNYE3K
kind: concept
name: Matrix of a linear map
msc: [15A04]
sources:
  - url: https://en.wikipedia.org/wiki/Transformation_matrix
    locator: lead section
same_as:
  wikidata: Q1482183
  wikipedia: Transformation matrix
---

## Summary

The matrix of a linear map in two bases is a matrix with one column for each basis vector of the domain.
Its column $j$ is the coordinate vector of the image of basis vector $j$.