Theorems · Theorem · linear algebra
Submodule.range_projection
∀ {R : Type u_1} [inst : Ring R] {E : Type u_2} [inst_1 : AddCommGroup E] [inst_2 : Module R E] {p q : Submodule R E}
(hpq : IsCompl p q), (p.projection q hpq).range = p- Defined in
- Mathlib.LinearAlgebra.Projection
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- RingAddCommGroupModule
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement · cited by 18,349
- AddCommGroupstatement and proof · cited by 12,871
- Top.topproof · cited by 9,680
- Ringstatement and proof · cited by 7,463
- Submodulestatement and proof · cited by 7,192
- LinearMap.rangestatement and proof · cited by 893
- Submodule.subtypeproof · cited by 480
- IsComplstatement and proof · cited by 351
- Submodule.map_topproof · cited by 105
- Submodule.range_subtypeproof · cited by 82
- Submodule.projectionOntoproof · cited by 81
Cited by6
Results whose statement or proof uses this declaration.
- LinearMap.FiniteRangeSetoid.projection_equiv_id_iff_isNoetherianproof · cited by 2
- LinearMap.FiniteRangeSetoid.projection_equiv_zero_iff_isNoetherianproof · cited by 1
- LinearMap.IsSymmetricProjection.le_iff_range_le_rangeproof · cited by 1
- Submodule.IsCompl.projection_rangeproof · cited by 0
- Submodule.starProjection_le_starProjection_iffproof · cited by 0
- Submodule.range_projectionLproof · cited by 0