Theorems · Theorem · linear algebra

Module.Basis.det_comp

∀ {M : Type u_2} [inst : AddCommGroup M] {ι : Type u_4} [inst_1 : DecidableEq ι] [inst_2 : Fintype ι] {A : Type u_5}
  [inst_3 : CommRing A] [inst_4 : Module A M] (e : Module.Basis ι A M) (f : M →ₗ[A] M) (v : ι → M),
  e.det (⇑f ∘ v) = LinearMap.det f * e.det v

Defined in

Mathlib.LinearAlgebra.Determinant

Cited by

2 results in Mathlib

Foundations

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

Assumes

AddCommGroupDecidableEqFintypeCommRingModule