Theorems · Definition · linear algebra
LinearPMap.graph
{R : Type u_1} →
[inst : Ring R] →
{E : Type u_4} →
[inst_1 : AddCommGroup E] →
[inst_2 : Module R E] →
{F : Type u_5} → [inst_3 : AddCommGroup F] → [inst_4 : Module R F] → (E →ₗ.[R] F) → Submodule R (E × F)The graph of a LinearPMap viewed as a submodule on E × F.
- Defined in
- Mathlib.LinearAlgebra.LinearPMap
- Cited by
- 39 results in Mathlib
- Foundations
- Depth 26 from the axioms · uses propext, Quot.sound
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.
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement and proof · cited by 18,349
- AddCommGroupstatement and proof · cited by 12,871
- Ringstatement and proof · cited by 7,463
- Submodulestatement · cited by 7,192
- LinearMap.idproof · cited by 625
- Submodule.mapproof · cited by 614
- Submodule.subtypeproof · cited by 480
- LinearPMapstatement and proof · cited by 179
- LinearPMap.domainproof · cited by 167
- LinearMap.prodMapproof · cited by 44
- LinearPMap.toFunproof · cited by 34
Cited by42
Results whose statement or proof uses this declaration.
- LinearPMap.IsClosableproof · cited by 15
- LinearPMap.inverseproof · cited by 9
- LinearPMap.IsClosable.graph_closure_eq_closure_graphstatement and proof · cited by 6
- LinearPMap.IsClosedproof · cited by 6
- LinearPMap.inverse_graphstatement and proof · cited by 4
- LinearPMap.le_of_le_graphstatement and proof · cited by 4
- Submodule.toLinearPMap_graph_eqstatement and proof · cited by 4
- LinearPMap.mem_graph_iffstatement · cited by 4
- LinearPMap.eq_of_eq_graphstatement and proof · cited by 3
- LinearPMap.le_graph_of_lestatement and proof · cited by 3
- LinearPMap.IsClosable.leIsClosableproof · cited by 2
- LinearPMap.closure_inverse_graphstatement and proof · cited by 2