---
tag: 0BR3FY5Q8M
kind: concept
name: Quotient space
msc: [15A03]
sources:
  - url: https://en.wikipedia.org/wiki/Quotient_space_(linear_algebra)
    locator: Definition
same_as:
  wikidata: Q1393796
  wikipedia: Quotient space (linear algebra)
---

## Summary

The quotient space of a vector space by a subspace is the set of cosets of the subspace, with the operations inherited from the space.
It identifies two vectors when their difference lies in the subspace.