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Theorems · Theorem · linear algebra

Module.Basis.coe_reindex

∀ {ι : Type u_1} {ι' : Type u_2} {R : Type u_3} {M : Type u_6} [inst : Semiring R] [inst_1 : AddCommMonoid M]
  [inst_2 : Module R M] (b : Module.Basis ι R M) (e : ι ≃ ι'), ⇑(b.reindex e) = ⇑b ∘ ⇑e.symm
Defined in
Mathlib.LinearAlgebra.Basis.Defs
Cited by
27 results in Mathlib
Foundations
Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
SemiringAddCommMonoidModule

Around this declaration

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

Module.Basis.equiv_apply · cited by 13Basis.equiv_applyAlgebra.FormallyUnramified.finite_of_free · cited by 7FormallyUnramified.finite…Module.Basis.baseChange_apply · cited by 7Basis.baseChange_applyAlgebra.discr_reindex · cited by 7Algebra.discr_reindexNumberField.canonicalEmbedding.latticeBasis_apply · cited by 7canonicalEmbedding.lattic…NumberField.mixedEmbedding.volume_fundamentalDomain_latticeBasis · cited by 4mixedEmbedding.volume_fun…NumberField.mixedEmbedding.volume_fundamentalDomain_fractionalIdealLatticeBasis · cited by 3mixedEmbedding.volume_fun…NumberField.Units.regOfFamily_eq_det' · cited by 3Units.regOfFamily_eq_det'NumberField.Units.basisOfIsMaxRank_apply · cited by 3Units.basisOfIsMaxRank_ap…Matrix.stdBasis_eq_single · cited by 3Matrix.stdBasis_eq_singleNumberField.discr_eq_discr · cited by 3NumberField.discr_eq_discrLinearMap.det_pi · cited by 2LinearMap.det_piNumberField.mixedEmbedding.fractionalIdealLatticeBasis_apply · cited by 2mixedEmbedding.fractional…NumberField.mixedEmbedding.fundamentalCone.linearIndependent_completeFamily · cited by 2fundamentalCone.linearInd…Module.Basis.map_equiv · cited by 2Basis.map_equivDFunLike.coe · cited by 62936DFunLike.coeModule · cited by 20661ModuleSemiring · cited by 13802SemiringAddCommMonoid · cited by 12281AddCommMonoidEquiv · cited by 8337EquivEquiv.symm · cited by 3681Equiv.symmModule.Basis · cited by 1477Module.BasisModule.Basis.reindex · cited by 57Basis.reindexModule.Basis.reindex_apply · cited by 7Basis.reindex_applyBasis.coe_reindexCITED BYCITES

Cites9

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Cited by27

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