Theorems · Theorem · linear algebra

equiv_iff_sameRay

∀ {R : Type u_1} [inst : CommSemiring R] [inst_1 : PartialOrder R] [inst_2 : IsStrictOrderedRing R] {M : Type u_2}
  [inst_3 : AddCommMonoid M] [inst_4 : Module R M] {v₁ v₂ : RayVector R M},
  v₁ ≈ v₂ ↔ SameRay R ↑((RayVector.equiv R M) v₁) ↑((RayVector.equiv R M) v₂)

Equivalence of nonzero vectors, in terms of SameRay.

Defined in

Mathlib.LinearAlgebra.Ray

Cited by

0 results in Mathlib

Foundations

Depth 29 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringPartialOrderIsStrictOrderedRingAddCommMonoidModule