Mathlib Map

Theorems · Theorem · linear algebra

LinearMap.BilinForm.flip_apply

∀ {R : Type u_1} {M : Type u_2} [inst : CommSemiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]
  (A : LinearMap.BilinForm R M) (x y : M), ((LinearMap.BilinForm.flipHom A) x) y = (A y) x
Defined in
Mathlib.LinearAlgebra.BilinearForm.Basic
Cited by
1 results in Mathlib
Foundations
Depth 38 from the axioms · uses propext, Quot.sound
Assumes
CommSemiringAddCommMonoidModule
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

LinearMap.BilinForm.isSymm_iff_flip · cited by 1BilinForm.isSymm_iff_flipDFunLike.coe · cited by 62936DFunLike.coeModule · cited by 20661ModuleRingHom.id · cited by 18349RingHom.idAddCommMonoid · cited by 12281AddCommMonoidCommSemiring · cited by 10911CommSemiringLinearMap · cited by 10215LinearMapLinearEquiv · cited by 3317LinearEquivLinearMap.BilinForm · cited by 501LinearMap.BilinFormLinearMap.BilinForm.flipHom · cited by 3BilinForm.flipHomBilinForm.flip_applyCITED BYCITES

Cites9

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by1

Results whose statement or proof uses this declaration.