##### Actions

A quadratic form $q$ on a vector space over a field $F$ which is non-degenerate (the associated bilinear form is non-singular) but which represents zero non-trivially: there is a non-zero vector $v$ such that $q(v) = 0$.
An anisotropic quadratic form' $q$ is one for which $q(v) = 0 \Rightarrow v=0$.