Theorems · Theorem · linear algebra
LinearMap.IsProj.isCompl
∀ {R : Type u_1} [inst : Ring R] {E : Type u_2} [inst_1 : AddCommGroup E] [inst_2 : Module R E] {p : Submodule R E}
{f : E →ₗ[R] E}, LinearMap.IsProj p f → IsCompl p f.ker- Defined in
- Mathlib.LinearAlgebra.Projection
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 68 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.
Cites12
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 and proof · cited by 18,349
- AddCommGroupstatement and proof · cited by 12,871
- LinearMapstatement and proof · cited by 10,215
- Ringstatement and proof · cited by 7,463
- Submodulestatement and proof · cited by 7,192
- LinearMap.kerstatement · cited by 848
- IsComplstatement and proof · cited by 351
- LinearMap.IsProjstatement and proof · cited by 23
- LinearMap.isCompl_of_projproof · cited by 5
- LinearMap.IsProj.codRestrict_apply_codproof · cited by 1
- LinearMap.IsProj.codRestrict_kerproof · cited by 1
Cited by6
Results whose statement or proof uses this declaration.
- LinearMap.IsIdempotentElem.isComplproof · cited by 4
- LinearMap.IsProj.traceproof · cited by 3
- LinearMap.IsProj.eq_conj_prodMapstatement and proof · cited by 1
- LinearMap.IsProj.eq_conj_prod_map'statement and proof · cited by 1
- LinearMap.IsIdempotentElem.isSymmetric_iff_isOrtho_range_kerproof · cited by 1
- LinearMap.isIdempotentElem_iff_eq_projection_range_kerproof · cited by 1