Theorems · Theorem · linear algebra

LinearMap.det_baseChange

∀ {R : Type u_3} {M : Type u_2} [inst : CommRing R] [inst_1 : AddCommGroup M] [inst_2 : Module R M] [Module.Free R M]
  [Module.Finite R M] (f : M →ₗ[R] M) {A : Type u_1} [inst_5 : CommRing A] [inst_6 : Algebra R A],
  LinearMap.det (LinearMap.baseChange A f) = (algebraMap R A) (LinearMap.det f)

Defined in

Mathlib.LinearAlgebra.Charpoly.BaseChange

Cited by

1 results in Mathlib

Foundations

Depth 131 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingAddCommGroupModuleModule.FreeModule.FiniteCommRingAlgebra