Theorems · Definition · linear algebra
LinearMap.lsmul
(R : Type u_2) → [inst : CommSemiring R] → (M : Type u_5) → [inst_1 : AddCommMonoid M] → [inst_2 : Module R M] → R →ₗ[R] M →ₗ[R] M
Scalar multiplication as a bilinear map R → M → M.
- Defined in
- Mathlib.LinearAlgebra.BilinearMap
- Cited by
- 50 results in Mathlib
- Foundations
- Depth 36 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- AddCommMonoidstatement and proof · cited by 12,281
- CommSemiringstatement and proof · cited by 10,911
- LinearMapstatement · cited by 10,215
- LinearMap.mk₂proof · cited by 5
Cited by64
Results whose statement or proof uses this declaration.
- TensorProduct.lidproof · cited by 96
- TensorProduct.ridproof · cited by 63
- Orientation.kahlerproof · cited by 39
- ModuleCat.smulShortComplexproof · cited by 11
- AdicCompletion.ofTensorProductproof · cited by 10
- Derivation.tensorProductToproof · cited by 10
- LinearMap.lsmul_injectivestatement · cited by 3
- IsSMulRegular.of_flat_of_isBaseChangeproof · cited by 3
- Convex.smulproof · cited by 3
- TensorProduct.lid'proof · cited by 3
- isSMulRegular_on_quot_iff_lsmul_comap_lestatement · cited by 3
- Submodule.exists_sub_one_mem_and_smul_eq_zero_of_fg_of_le_smulproof · cited by 3