---
tag: 00KDZRW4C0
kind: concept
name: Determinant
msc: [15A15]
sources:
  - url: https://en.wikipedia.org/wiki/Determinant
    locator: As an alternating multilinear form
same_as:
  wikidata: Q178546
  wikipedia: Determinant
---

## Summary

The determinant is the unique function of square matrices that is multilinear and alternating in the rows and is $1$ on the identity matrix.
It is zero exactly for the singular matrices, over a field.