English
There is a canonical identity isometry from a quadratic form to itself, which acts as the identity on its underlying vector space and whose action on the quadratic form is trivial.
Русский
Существует каноническая идентичная изометрия от квадратичной формы к самой себе, действующая как тождественное отображение на базовом векторном пространстве.
LaTeX
$$$\mathrm{id}(Q) : Q \to qᵢ Q$ with $(\mathrm{id}(Q))(m) = m$ for all $m$, and underlying linear map $\mathrm{LinearMap.id}$$$
Lean4
/-- The identity isometry from a quadratic form to itself. -/
@[simps!]
def id (Q : QuadraticMap R M N) : Q →qᵢ Q where
__ := LinearMap.id
map_app' _ := rfl