Hermitian form over a quadratic finite field
= Hermitian form over a quadratic finite field
{c}
{title2=$B(v,w)=\overline{B(w,v)},\quad\bar a=a^q$}
Over the <finite field> $K=\mathbb F_{q^2}$, a <sesquilinear form> relative to $a\mapsto a^q$ is linear in its first argument and conjugate-linear in its second. It is Hermitian when $B(w,v)=\overline{B(v,w)}$. Its diagonal values belong to $\mathbb F_q$; it is nondegenerate when $B(v,w)=0$ for every $w$ forces $v=0$. This definition applies in characteristic two as well.