Isometry of a space with a form
= Isometry of a space with a form
A linear bijection between spaces carrying compatible <bilinear forms>, <Hermitian forms> or <quadratic forms> is an <isometry of a space with a form> when it preserves the specified form. Preserving the polar form alone need not preserve a <quadratic form> in characteristic two. Subspaces may have degenerate restricted forms even when the ambient form is nonsingular.