Theorems · Theorem · linear algebra
LinearMap.IsProj.mem_invtSubmodule_iff
∀ {E : Type u_1} {R : Type u_2} [inst : Ring R] [inst_1 : AddCommGroup E] [inst_2 : Module R E] {T f : E →ₗ[R] E}
{U : Submodule R E}, LinearMap.IsProj U f → (U ∈ Module.End.invtSubmodule T ↔ f ∘ₗ T ∘ₗ f = T ∘ₗ f)- Defined in
- Mathlib.LinearAlgebra.Projection
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- RingAddCommGroupModule
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Cites13
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.compstatement · cited by 1,642
- Sublatticestatement · cited by 225
- Module.End.invtSubmodulestatement · cited by 93
- LinearMap.IsProjstatement and proof · cited by 23
- LinearMap.IsIdempotentElem.range_mem_invtSubmodule_iffproof · cited by 5
- LinearMap.IsProj.rangeproof · cited by 3
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