Theorems · Theorem · linear algebra

Module.Basis.orientation_unitsSMul

∀ {R : Type u_1} [inst : CommRing R] [inst_1 : PartialOrder R] [inst_2 : IsStrictOrderedRing R] {M : Type u_2}
  [inst_3 : AddCommGroup M] [inst_4 : Module R M] {ι : Type u_4} [inst_5 : Fintype ι] [inst_6 : DecidableEq ι]
  (e : Module.Basis ι R M) (w : ι → Rˣ), (e.unitsSMul w).orientation = (∏ i, w i)⁻¹ • e.orientation

The orientation given by a basis derived using units_smul, in terms of the product of those units.

Defined in

Mathlib.LinearAlgebra.Orientation

Cited by

1 results in Mathlib

Foundations

Depth 99 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingPartialOrderIsStrictOrderedRingAddCommGroupModuleFintypeDecidableEq