---
tag: 05CJSSXPR3
kind: concept
name: Determinant of a family of vectors in a basis
msc: [15A15, 15A75]
sources:
  - url: https://en.wikipedia.org/wiki/Determinant
    locator: Determinant of n vectors
---

## Summary

The determinant of a family of $n$ vectors in a basis of an $n$-dimensional space is a scalar.
It is the determinant of the matrix of their coordinates in that basis.