Theorems · Theorem · linear algebra

LinearMap.BilinForm.apply_toDual_symm_apply

∀ {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} {hB : B.Nondegenerate} (f : Module.Dual K V) (v : V),
  (B ((B.toDual hB).symm f)) v = f v

Defined in: Mathlib.LinearAlgebra.BilinearForm.Properties
Cited by: 1 results in Mathlib
Foundations: Depth 122 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Field AddCommGroup Module FiniteDimensional

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

DFunLike.coestatement and proof · 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
LinearEquiv.symmstatement · cited by 1,461
Module.Dualstatement and proof · cited by 583
LinearMap.BilinFormstatement and proof · cited by 501
LinearEquiv.apply_symm_applyproof · cited by 108

Cited by1

Results whose statement or proof uses this declaration.

LieAlgebra.IsKilling.lie_eq_killingForm_smul_of_mem_rootSpace_of_mem_rootSpace_neg_auxproof · cited by 2