Theorems · Theorem · linear algebra
LinearMap.graph_eq_range_prod
∀ {R : Type u} {M : Type v} {M₂ : Type w} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : AddCommMonoid M₂]
[inst_3 : Module R M] [inst_4 : Module R M₂] (f : M →ₗ[R] M₂), f.graph = (LinearMap.id.prod f).range- Defined in
- Mathlib.LinearAlgebra.Prod
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 27 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.
- 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
- Submodulestatement · cited by 7,192
- LinearMap.rangestatement and proof · cited by 893
- LinearMap.idstatement and proof · cited by 625
- Submodule.extproof · cited by 204
- LinearMap.prodstatement and proof · cited by 32
- LinearMap.graphstatement and proof · cited by 13
Cited by1
Results whose statement or proof uses this declaration.
- LinearMap.continuous_of_isClosed_graphproof · cited by 1