Theorems · Theorem · linear algebra

Module.Basis.det_unitsSMul_self

∀ {R : Type u_1} [inst : CommRing R] {M : Type u_2} [inst_1 : AddCommGroup M] [inst_2 : Module R M] {ι : Type u_4}
  [inst_3 : DecidableEq ι] [inst_4 : Fintype ι] (e : Module.Basis ι R M) (w : ι → Rˣ),
  e.det ⇑(e.unitsSMul w) = ∏ i, ↑(w i)

The determinant of a basis constructed by unitsSMul is the product of the given units.

Defined in

Mathlib.LinearAlgebra.Determinant

Cited by

2 results in Mathlib

Foundations

Depth 94 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingAddCommGroupModuleDecidableEqFintype