Orthogonal group over a finite field
= Orthogonal group over a finite field
{title2=$O(V,Q)=\{g\in GL(V):Q(gv)=Q(v)\}$}
The <group> of invertible <linear maps> preserving a specified <quadratic form> over a <finite field>. In characteristic two one must preserve the <quadratic form> itself, not merely its polar <alternating bilinear form>. For a nonsingular form, any two nonzero <isotropic vectors> can be incorporated into hyperbolic pairs and standard adapted bases, producing an isometry between them.