Theorems · Definition · linear algebra
LinearMap.graph
{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] → (M →ₗ[R] M₂) → Submodule R (M × M₂)Graph of a linear map.
- Defined in
- Mathlib.LinearAlgebra.Prod
- Cited by
- 13 results in Mathlib
- Foundations
- Depth 23 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- Set.ofPredproof · cited by 6,101
Cited by15
Results whose statement or proof uses this declaration.
- LinearPMap.graphproof · cited by 39
- LinearMap.exists_range_eq_graphstatement · cited by 2
- ContinuousLinearMap.ofIsClosedGraphstatement and proof · cited by 2
- LinearMap.exists_linearEquiv_eq_graphstatement and proof · cited by 1
- LinearMap.continuous_of_isClosed_graphstatement and proof · cited by 1
- LinearMap.continuous_of_seq_closed_graphproof · cited by 1
- LinearMap.mem_graph_iffstatement · cited by 1
- Submodule.goursat_surjectivestatement and proof · cited by 1
- LinearMap.graph_eq_range_prodstatement and proof · cited by 1
- ContinuousLinearMap.coe_ofIsClosedGraphstatement and proof · cited by 0
- Submodule.exists_eq_graphstatement and proof · cited by 0
- Submodule.exists_equiv_eq_graphstatement and proof · cited by 0