Mathlib Map

Theorems · Definition · linear algebra

LinearMap.GeneralLinearGroup.ofLinearEquiv

{R : Type u_1} →
  {M : Type u_2} →
    [inst : Semiring R] →
      [inst_1 : AddCommMonoid M] → [inst_2 : Module R M] → (M ≃ₗ[R] M) → LinearMap.GeneralLinearGroup R M

An equivalence from M to itself determines an invertible linear map.

Defined in
Mathlib.LinearAlgebra.GeneralLinearGroup.Basic
Cited by
6 results in Mathlib
Foundations
Depth 29 from the axioms · uses propext, Quot.sound
Assumes
SemiringAddCommMonoidModule
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

LinearMap.GeneralLinearGroup.generalLinearEquiv · cited by 7GeneralLinearGroup.genera…Matrix.UnitaryGroup.toGL · cited by 3UnitaryGroup.toGLLinearMap.GeneralLinearGroup.ofLinearEquiv_smul · cited by 0GeneralLinearGroup.ofLine…LinearMap.GeneralLinearGroup.coe_ofLinearEquiv · cited by 0GeneralLinearGroup.coe_of…LinearMap.GeneralLinearGroup.congrLinearEquiv_apply · cited by 0GeneralLinearGroup.congrL…Module.End.mulSemiringActionToAlgEquiv_conjAct_surjective · cited by 0End.mulSemiringActionToAl…LinearMap.GeneralLinearGroup.ofLinearEquiv_inv · cited by 0GeneralLinearGroup.ofLine…LinearMap.GeneralLinearGroup.ofLinearEquiv_mul · cited by 0GeneralLinearGroup.ofLine…Module · cited by 20661ModuleRingHom.id · cited by 18349RingHom.idSemiring · cited by 13802SemiringAddCommMonoid · cited by 12281AddCommMonoidLinearEquiv · cited by 3317LinearEquivLinearEquiv.symm · cited by 1461LinearEquiv.symmLinearEquiv.toLinearMap · cited by 1171LinearEquiv.toLinearMapLinearMap.GeneralLinearGroup · cited by 27LinearMap.GeneralLinearGr…GeneralLinearGroup.ofLinearEq…CITED BYCITES

Cites8

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

Cited by8

Results whose statement or proof uses this declaration.