Theorems · Theorem · linear algebra

ray_eq_iff

∀ {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 : M} (hv₁ : v₁ ≠ 0) (hv₂ : v₂ ≠ 0),
  rayOfNeZero R v₁ hv₁ = rayOfNeZero R v₂ hv₂ ↔ SameRay R v₁ v₂

The rays given by two nonzero vectors are equal if and only if those vectors satisfy SameRay.

Defined in

Mathlib.LinearAlgebra.Ray

Cited by

8 results in Mathlib

Foundations

Depth 31 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringPartialOrderIsStrictOrderedRingAddCommMonoidModule