Theorems · Definition · linear algebra

LinearEquiv.ofIsUnitDet

{R : Type u_1} →
  [inst : CommRing R] →
    {M : Type u_2} →
      [inst_1 : AddCommGroup M] →
        [inst_2 : Module R M] →
          {M' : Type u_3} →
            [inst_3 : AddCommGroup M'] →
              [inst_4 : Module R M'] →
                {ι : Type u_4} →
                  [inst_5 : DecidableEq ι] →
                    [inst_6 : Fintype ι] →
                      {f : M →ₗ[R] M'} →
                        {v : Module.Basis ι R M} →
                          {v' : Module.Basis ι R M'} → IsUnit ((LinearMap.toMatrix v v') f).det → M ≃ₗ[R] M'

Builds a linear equivalence from a linear map whose determinant in some bases is a unit.

Defined in

Mathlib.LinearAlgebra.Determinant

Cited by

7 results in Mathlib

Foundations

Depth 107 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingAddCommGroupModuleAddCommGroupModuleDecidableEqFintype