Theorems · Definition · linear algebra
LinearMap.inl
(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] M × M₂The left injection into a product is a linear map.
- Defined in
- Mathlib.LinearAlgebra.Prod
- Cited by
- 72 results in Mathlib
- Foundations
- Depth 24 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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 · cited by 18,349
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- LinearMapstatement · cited by 10,215
- LinearMap.idproof · cited by 625
- LinearMap.prodproof · cited by 32
Cited by81
Results whose statement or proof uses this declaration.
- LinearMap.prod_extstatement and proof · cited by 14
- Module.Basis.prod_applystatement · cited by 11
- CliffordAlgebra.EquivEven.vproof · cited by 11
- LieHom.inlproof · cited by 10
- QuadraticMap.Isometry.inlproof · cited by 5
- UniqueDiffWithinAt.prodproof · cited by 4
- LinearMap.prodOfFinsuppNatproof · cited by 4
- Function.Exact.splitSurjectiveEquivstatement and proof · cited by 4
- LinearMap.coprodEquivproof · cited by 4
- LinearMap.coprod_inl_inrstatement · cited by 4
- LinearMap.range_inlstatement and proof · cited by 3
- LinearIsometry.inlproof · cited by 3