Theorems · Theorem · linear algebra

Module.Basis.map_equiv

∀ {ι' : Type u_2} {M' : Type u_7} [inst : AddCommMonoid M'] {ι : Type u_10} {R : Type u_11} {M : Type u_12}
  [inst_1 : Semiring R] [inst_2 : AddCommMonoid M] [inst_3 : Module R M] [inst_4 : Module R M'] (b : Module.Basis ι R M)
  (b' : Module.Basis ι' R M') (e : ι ≃ ι'), b.map (b.equiv b' e) = b'.reindex e.symm

Defined in

Mathlib.LinearAlgebra.Basis.Defs

Cited by

2 results in Mathlib

Foundations

Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddCommMonoidSemiringAddCommMonoidModuleModule