Theorems · Theorem · linear algebra
LinearMap.BilinForm.toDual_def
∀ {V : Type u_5} {K : Type u_6} [inst : Field K] [inst_1 : AddCommGroup V] [inst_2 : Module K V]
[inst_3 : FiniteDimensional K V] {B : LinearMap.BilinForm K V} (b : B.Nondegenerate) {m n : V},
((B.toDual b) m) n = (B m) n- Cited by
- 2 results in Mathlib
- Foundations
- Depth 122 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement · cited by 18,349
- AddCommGroupstatement and proof · cited by 12,871
- LinearMapstatement · cited by 10,215
- Fieldstatement and proof · cited by 7,404
- LinearEquivstatement · cited by 3,317
- FiniteDimensionalstatement and proof · cited by 1,854
- Module.Dualstatement · cited by 583
- LinearMap.BilinFormstatement and proof · cited by 501
- LinearMap.BilinForm.Nondegeneratestatement and proof · cited by 77
- LinearMap.BilinForm.toDualstatement · cited by 7
Cited by2
Results whose statement or proof uses this declaration.
- LinearMap.BilinForm.apply_dualBasis_leftproof · cited by 5
- LinearMap.BilinForm.dualBasis_repr_applyproof · cited by 4