Theorems · Theorem · linear algebra

Module.Basis.equivFun_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]
  [inst_3 : Finite ι] [inst_4 : DecidableEq ι] (b : Module.Basis ι R M) (i j : ι),
  b.equivFun (b i) j = if i = j then 1 else 0

Defined in: Mathlib.LinearAlgebra.Basis.Defs
Cited by: 1 results in Mathlib
Foundations: Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Semiring AddCommMonoid Module Finite DecidableEq

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Cites11

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

DFunLike.coestatement and proof · 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
LinearEquivstatement · cited by 3,317
Finitestatement and proof · cited by 3,029
Module.Basisstatement and proof · cited by 1,477
Module.Basis.equivFunstatement · cited by 88
Module.Basis.repr_self_applyproof · cited by 9
Module.Basis.equivFun_applyproof · cited by 7

Cited by1

Results whose statement or proof uses this declaration.

Module.Finite.of_finite_tensorProduct_of_faithfullyFlatproof · cited by 2