Definition:Relative Matrix of Quadratic Form

Definition
Let $K$ be a field of characteristic $\Char K \ne 2$.

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

Let $\BB$ be an ordered basis of $V$.

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

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