---
tag: 094V2VBJXJ
kind: concept
name: Multiplication by a matrix as a linear map
msc: [15A04]
sources:
  - url: https://en.wikipedia.org/wiki/Transformation_matrix
    locator: Uses
---

## Summary

Each $m \times n$ matrix $A$ defines the linear map from $F^n$ to $F^m$ that sends a column vector $x$ to the product $Ax$.