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.
Cites9
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
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- Equivstatement and proof · cited by 8,337
- Equiv.symmstatement · cited by 3,681
- Module.Basisstatement and proof · cited by 1,477
- Module.Basis.reindexstatement · cited by 57
- Module.Basis.reindex_applyproof · cited by 7
Cited by27
Results whose statement or proof uses this declaration.
- Module.Basis.equiv_applyproof · cited by 13
- Algebra.FormallyUnramified.finite_of_freeproof · cited by 7
- Module.Basis.baseChange_applyproof · cited by 7
- Algebra.discr_reindexproof · cited by 7
- NumberField.canonicalEmbedding.latticeBasis_applyproof · cited by 7
- NumberField.mixedEmbedding.volume_fundamentalDomain_latticeBasisproof · cited by 4
- NumberField.Units.regOfFamily_eq_det'proof · cited by 3
- NumberField.Units.basisOfIsMaxRank_applyproof · cited by 3
- Matrix.stdBasis_eq_singleproof · cited by 3
- NumberField.discr_eq_discrproof · cited by 3
- LinearMap.det_piproof · cited by 2