Theorems · Theorem · group theory

Matrix.SpecialLinearGroup.map_mapGL

∀ {n : Type u} [inst : DecidableEq n] [inst_1 : Fintype n] {R : Type v} [inst_2 : CommRing R] {S : Type u_1}
  [inst_3 : CommRing S] [inst_4 : Algebra R S] {T : Type u_2} [inst_5 : CommRing T] [inst_6 : Algebra R T]
  [inst_7 : Algebra S T] [IsScalarTower R S T] (g : Matrix.SpecialLinearGroup n R),
  (Matrix.GeneralLinearGroup.map (algebraMap S T)) ((Matrix.SpecialLinearGroup.mapGL S) g) =
    (Matrix.SpecialLinearGroup.mapGL T) g

Defined in

Mathlib.LinearAlgebra.Matrix.GeneralLinearGroup.Defs

Cited by

3 results in Mathlib

Foundations

Depth 108 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

DecidableEqFintypeCommRingCommRingAlgebraCommRingAlgebraAlgebraIsScalarTower