Theorems · Theorem · linear algebra
Module.Basis.repr_self
∀ {ι : Type u_1} {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) (i : ι), b.repr (b i) = fun₀ | i => 1- Defined in
- Mathlib.LinearAlgebra.Basis.Defs
- Cited by
- 82 results in Mathlib
- Foundations
- Depth 79 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.
Cites11
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
- RingHom.idstatement · cited by 18,349
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- Finsuppstatement · cited by 5,255
- LinearEquivstatement · cited by 3,317
- Module.Basisstatement and proof · cited by 1,477
- Finsupp.singlestatement and proof · cited by 943
- Module.Basis.reprstatement and proof · cited by 498
- LinearEquiv.apply_symm_applyproof · cited by 108
Cited by82
Results whose statement or proof uses this declaration.
- Module.Basis.constr_basisproof · cited by 17
- Module.Basis.equiv_applyproof · cited by 13
- Module.Basis.apply_eq_iffproof · cited by 12
- Matrix.toLin_selfproof · cited by 9
- Module.Basis.repr_self_applyproof · cited by 9
- Module.Basis.toMatrix_selfproof · cited by 8
- LinearMap.toMatrix_idproof · cited by 7
- LinearMap.BilinForm.apply_dualBasis_leftproof · cited by 5
- Module.Basis.restrictScalars_repr_applyproof · cited by 5
- Module.End.mem_center_iffproof · cited by 4
- Module.Basis.ofZLatticeBasis_repr_applyproof · cited by 4
- Algebra.Generators.CotangentSpace.compEquiv_symm_inrproof · cited by 4