Theorems · Theorem · linear algebra

LinearMap.det_smul

∀ {M : Type u_2} [inst : AddCommGroup M] {A : Type u_5} [inst_1 : CommRing A] [inst_2 : Module A M] [Module.Free A M]
  (c : A) (f : M →ₗ[A] M), LinearMap.det (c • f) = c ^ Module.finrank A M * LinearMap.det f

Multiplying a map by a scalar c multiplies its determinant by c ^ dim M.

Defined in

Mathlib.LinearAlgebra.Determinant

Cited by

5 results in Mathlib

Foundations

Depth 130 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddCommGroupCommRingModuleModule.Free