Theorems · Theorem · linear algebra
LinearMap.IsProj.codRestrict_ker
∀ {S : Type u_5} [inst : Semiring S] {M : Type u_6} [inst_1 : AddCommMonoid M] [inst_2 : Module S M] {m : Submodule S M}
{f : M →ₗ[S] M} (h : LinearMap.IsProj m f), h.codRestrict.ker = f.ker- Defined in
- Mathlib.LinearAlgebra.Projection
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 29 from the axioms · uses propext, Quot.sound
- Assumes
- SemiringAddCommMonoidModule
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- LinearMapstatement and proof · cited by 10,215
- Submodulestatement and proof · cited by 7,192
- LinearMap.kerstatement · cited by 848
- LinearMap.IsProjstatement and proof · cited by 23
- LinearMap.ker_codRestrictproof · cited by 11
- LinearMap.IsProj.codRestrictstatement · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- LinearMap.IsProj.isComplproof · cited by 6