Theorems · Theorem · linear algebra
Module.Basis.equivFun_apply
∀ {ι : Type u_1} {R : Type u_3} {M : Type u_6} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]
[inst_3 : Finite ι] (b : Module.Basis ι R M) (u : M), b.equivFun u = ⇑(b.repr u)- Defined in
- Mathlib.LinearAlgebra.Basis.Defs
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound
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
- Finitestatement and proof · cited by 3,029
- Module.Basisstatement and proof · cited by 1,477
- Module.Basis.reprstatement · cited by 498
- Module.Basis.equivFunstatement · cited by 88
Cited by7
Results whose statement or proof uses this declaration.
- Algebra.norm_eq_zero_iffproof · cited by 6
- LinearMap.toMatrix_mulVec_reprproof · cited by 5
- IsAdjoinRootMonic.ext_elemproof · cited by 2
- Algebra.discr_mul_isIntegral_mem_adjoinproof · cited by 1
- Module.Basis.equivFun_selfproof · cited by 1
- Module.Basis.toDual_eq_equivFunproof · cited by 0
- Module.Basis.dualBasis_equivFunproof · cited by 0