Theorems · Theorem · linear algebra
finrank_span_singleton
∀ {K : Type u} {V : Type v} [inst : DivisionRing K] [inst_1 : AddCommGroup V] [inst_2 : Module K V] {v : V},
v ≠ 0 → Module.finrank K ↥(K ∙ v) = 1- Cited by
- 16 results in Mathlib
- Foundations
- Depth 117 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- Submodulestatement · cited by 7,192
- le_antisymmproof · cited by 2,068
- Module.finrankstatement · cited by 1,770
- Submodule.spanstatement · cited by 1,504
- DivisionRingstatement and proof · cited by 1,062
- Submodule.mem_span_singleton_selfproof · cited by 59
- Subtype.coe_ne_coeproof · cited by 27
- Module.finrank_pos_iffproof · cited by 8
- finrank_span_le_cardproof · cited by 8
Cited by16
Results whose statement or proof uses this declaration.
- EuclideanGeometry.Sphere.finrank_orthRadiusproof · cited by 3
- Submodule.finrank_sup_span_singletonproof · cited by 2
- LinearMap.BilinForm.exists_orthogonal_basisproof · cited by 2
- EuclideanGeometry.Sphere.inter_orthRadius_eq_empty_of_finrank_eq_oneproof · cited by 1
- Matrix.SpecialLinearGroup.lineStab_fix_of_spanproof · cited by 1
- eq_span_singleton_of_mem_of_finrank_eq_oneproof · cited by 1
- Submodule.sup_span_singleton_eq_top_iffproof · cited by 1
- Submodule.isAtom_iff_finrank_eq_oneproof · cited by 1
- SchauderBasis.RankOneDecomposition.exists_coeffproof · cited by 1
- exists_smul_eq_of_finrank_eq_oneproof · cited by 1
- Submodule.finrank_orthogonal_span_singletonproof · cited by 1
- Projectivization.finrank_submoduleproof · cited by 1