Theorems · Definition · ring theory
LinearMap.id
{R : Type u_1} → {M : Type u_8} → [inst : Semiring R] → [inst_1 : AddCommMonoid M] → [inst_2 : Module R M] → M →ₗ[R] MIdentity map as a LinearMap
- Defined in
- Mathlib.Algebra.Module.LinearMap.Defs
- Cited by
- 625 results in Mathlib
- Foundations
- Depth 17 from the axioms, rests on 157 definitions · uses no axioms
- Assumes
- SemiringAddCommMonoidModule
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.
- 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
- MonoidHom.idproof · cited by 323
- DistribMulActionHomproof · cited by 63
- DistribMulActionHom.idproof · cited by 3
Cited by721
Results whose statement or proof uses this declaration.
- Finsupp.linearCombinationproof · cited by 269
- LinearMap.rTensorproof · cited by 266
- AffineMap.lineMapproof · cited by 254
- ContinuousLinearMap.idproof · cited by 233
- LinearMap.lTensorproof · cited by 203
- LinearEquiv.reflproof · cited by 143
- LinearMap.toSpanSingletonproof · cited by 78
- LinearMap.inlproof · cited by 72
- Orientation.rotationproof · cited by 62
- LinearMap.inrproof · cited by 62
- LinearMap.baseChangeproof · cited by 62
- Module.Dual.evalproof · cited by 52
Showing the 200 most cited of 721.