Theorems · Theorem · linear algebra

Module.Basis.det_comp_basis

∀ {M : Type u_2} [inst : AddCommGroup M] {M' : Type u_3} [inst_1 : AddCommGroup M'] {ι : Type u_4}
  [inst_2 : DecidableEq ι] [inst_3 : Fintype ι] {A : Type u_5} [inst_4 : CommRing A] [inst_5 : Module A M]
  [inst_6 : Module A M'] (b : Module.Basis ι A M) (b' : Module.Basis ι A M') (f : M →ₗ[A] M'),
  b'.det (⇑f ∘ ⇑b) = LinearMap.det (f ∘ₗ ↑(b'.equiv b (Equiv.refl ι)))

Defined in

Mathlib.LinearAlgebra.Determinant

Cited by

2 results in Mathlib

Foundations

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

Assumes

AddCommGroupAddCommGroupDecidableEqFintypeCommRingModuleModule