Theorems · Theorem · linear algebra
LinearMap.IsIdempotentElem.isProj_range
∀ {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),
IsIdempotentElem f → LinearMap.IsProj f.range fAlias of the reverse direction of LinearMap.isProj_range_iff_isIdempotentElem.
- Defined in
- Mathlib.LinearAlgebra.Projection
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 28 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.
Cites9
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
- LinearMap.rangestatement · cited by 893
- IsIdempotentElemstatement · cited by 217
- LinearMap.IsProjstatement · cited by 23
- LinearMap.isProj_range_iff_isIdempotentElemproof · cited by 1
Cited by8
Results whose statement or proof uses this declaration.
- LinearMap.IsIdempotentElem.eq_projectionproof · cited by 5
- LinearMap.IsIdempotentElem.isComplproof · cited by 4
- LinearMap.IsIdempotentElem.mem_range_iffproof · cited by 3
- LinearMap.IsProj.rangeproof · cited by 3
- LinearMap.IsIdempotentElem.isSymmetric_iff_isOrtho_range_kerproof · cited by 1
- LinearMap.isIdempotentElem_iff_eq_projection_range_kerproof · cited by 1
- LinearMap.IsIdempotentElem.trace_eq_zero_iffproof · cited by 1
- LinearMap.isProj_iff_isIdempotentElemproof · cited by 1