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Theorems · Theorem · geometry

Projectivization.exists_not_self_orthogonal

∀ {F : Type u_1} [inst : Field F] {m : Type u_2} [inst_1 : Fintype m] (v : Projectivization F (m → F)),
  ∃ w, ¬v.orthogonal w
Defined in
Mathlib.LinearAlgebra.Projectivization.Constructions
Cited by
1 results in Mathlib
Foundations
Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
FieldFintype
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Projectivization.exists_not_orthogonal_self · cited by 0Projectivization.exists_n…Fintype · cited by 7736FintypeField · cited by 7404FielddotProduct · cited by 194dotProductProjectivization · cited by 111ProjectivizationProjectivization.mk · cited by 55Projectivization.mkProjectivization.ind · cited by 15Projectivization.inddotProduct_zero · cited by 11dotProduct_zeroProjectivization.orthogonal · cited by 10Projectivization.orthogon…dotProduct_eq_zero_iff · cited by 1dotProduct_eq_zero_iffProjectivization.exists_not_s…CITED BYCITES

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Cited by1

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