---
tag: 0QJJAQ6ZYZ
kind: concept
name: Orientation of a real vector space
msc: [15A04, 15A15]
sources:
  - url: https://en.wikipedia.org/wiki/Orientation_(vector_space)
    locator: Definition
same_as:
  wikidata: Q107472979
  wikipedia: Orientation (vector space)
---

## Summary

An orientation of a finite-dimensional real vector space is a choice of one of the two classes of ordered bases.
Two bases are in the same class when the change of basis matrix has positive determinant.