Theorems · Theorem · linear algebra
LinearMap.IsIdempotentElem.comp_eq_left_iff
∀ {S : Type u_5} [inst : Semiring S] {M : Type u_7} [inst_1 : AddCommGroup M] [inst_2 : Module S M] {q : M →ₗ[S] M},
IsIdempotentElem q →
∀ {E : Type u_8} [inst_3 : AddCommGroup E] [inst_4 : Module S E] (p : M →ₗ[S] E), p ∘ₗ q = p ↔ q.ker ≤ p.ker- Defined in
- Mathlib.LinearAlgebra.Projection
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 49 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.
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement and proof · cited by 18,349
- Semiringstatement and proof · cited by 13,802
- AddCommGroupstatement and proof · cited by 12,871
- LinearMapstatement and proof · cited by 10,215
- Submodulestatement · cited by 7,192
- LinearMap.compstatement and proof · cited by 1,642
- LinearMap.kerstatement and proof · cited by 848
- LinearMap.idproof · cited by 625
- IsIdempotentElemstatement and proof · cited by 217
- LinearMap.comp_subproof · cited by 4
- LinearMap.IsIdempotentElem.ker_eq_rangeproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- LinearMap.IsIdempotentElem.ker_mem_invtSubmodule_iffproof · cited by 4