quadratic form

《Advanced Linear Algebra》 · 第 264 页 · Chapter 11「Quadratic Forms」

A quadratic form on a vector space $V$ is a map $q:V\to F$ such that $q(av)=a^2q(v)$ and the map $\langle u,v\rangle_q=q(u+v)-q(u)-q(v)$ is a symmetric bilinear form.