Theorems · Definition · linear algebra

Module.Basis.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] →
                  Module.Basis ι R M → [inst_4 : Module R M'] → Module.Basis ι' R M' → ι ≃ ι' → M ≃ₗ[R] M'

If b is a basis for M and b' a basis for M', and the index types are equivalent, b.equiv b' e is a linear equivalence M ≃ₗ[R] M', mapping b i to b' (e i).

Defined in

Mathlib.LinearAlgebra.Basis.Defs

Cited by

19 results in Mathlib

Foundations

Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddCommMonoidSemiringAddCommMonoidModuleModule