Theorems · Theorem · linear algebra
LinearMap.isProj_range_iff_isIdempotentElem
∀ {S : Type u_5} [inst : Semiring S] {M : Type u_6} [inst_1 : AddCommMonoid M] [inst_2 : Module S M] (f : M →ₗ[S] M),
LinearMap.IsProj f.range f ↔ IsIdempotentElem f- Defined in
- Mathlib.LinearAlgebra.Projection
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 27 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SemiringAddCommMonoidModule
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- 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
- LinearMap.rangestatement and proof · cited by 893
- LinearMap.extproof · cited by 844
- IsIdempotentElemstatement and proof · cited by 217
- IsIdempotentElem.eqproof · cited by 42
- LinearMap.mem_range_selfproof · cited by 31
- Module.End.mul_applyproof · cited by 23
Cited by1
Results whose statement or proof uses this declaration.
- LinearMap.IsIdempotentElem.isProj_rangeproof · cited by 8