English
Given a nondegenerate bilinear form on a finite-dimensional vector space, B.toDual is a linear equivalence between the space and its dual.
Русский
Дано неdegenerate билинейная форма на конечномерном векторном пространстве, B.toDual — это линейное взаимнооднозначное отображение пространства и его двойстороны.
LaTeX
$$$\\text{nondegenerate } B \\Rightarrow B.toDual : V \\simeq\\_K V^*$$$
Lean4
/-- Given a nondegenerate bilinear form `B` on a finite-dimensional vector space, `B.toDual` is
the linear equivalence between a vector space and its dual. -/
noncomputable def toDual (B : BilinForm K V) (b : B.Nondegenerate) : V ≃ₗ[K] Module.Dual K V :=
B.linearEquivOfInjective (LinearMap.ker_eq_bot.mp <| b.ker_eq_bot) Subspace.dual_finrank_eq.symm
