---
tag: 0RBQS1JJCR
kind: concept
name: Quadratic form
msc: [15A63, "11E04"]
sources:
  - url: https://en.wikipedia.org/wiki/Quadratic_form
    locator: Definitions
same_as:
  wikidata: Q736753
  wikipedia: Quadratic form
---

## Summary

A quadratic form on a vector space is a map $Q$ to the scalars with $Q(av) = a^2 Q(v)$.
Also, $Q(u + v) - Q(u) - Q(v)$ must be bilinear in $u$ and $v$.
In coordinates, it is a homogeneous polynomial of degree two.