---
tag: 0N4F5FMQZW
kind: concept
name: Quotient map
aliases: [canonical-projection]
msc: [15A03, 15A04]
sources:
  - url: https://en.wikipedia.org/wiki/Quotient_space_(linear_algebra)
    locator: Definition
---

## Summary

The quotient map of a vector space onto a quotient space sends each vector to its coset.
It is a surjective linear map whose kernel is the subspace.