Definition:Relative Matrix of Quadratic Form

Definition
Let $\mathbb K$ be a field of characteristic $\operatorname{char}\mathbb K \neq2$.

Let $V$ be a vector space over $\mathbb K$ of finite dimension $n>0$.

Let $\mathcal B$ be an ordered basis of $V$.

Let $q$ be a quadratic form on $V$.

Its matrix relative to $\mathcal B$ is the matrix of its associated bilinear form relative to $\mathcal B$, denoted $\mathbf M_{q, \mathcal B}$.