Theorems · Theorem · linear algebra
LinearMap.toSpanSingleton_apply
∀ (R : Type u_1) (M : Type u_4) [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] (x : M) (b : R), (LinearMap.toSpanSingleton R M x) b = b • x
- Defined in
- Mathlib.LinearAlgebra.Span.Basic
- Cited by
- 38 results in Mathlib
- Foundations
- Depth 26 from the axioms · uses no axioms
- Assumes
- SemiringAddCommMonoidModule
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.
- DFunLike.coestatement and proof · cited by 62,936
- 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.toSpanSingletonstatement and proof · cited by 78
Cited by38
Results whose statement or proof uses this declaration.
- RootPairing.Polarization_applyproof · cited by 8
- IsLocalization.away_of_isIdempotentElemproof · cited by 4
- RootPairing.PolarizationIn_applyproof · cited by 4
- RootPairing.PolarizationIn_eqproof · cited by 4
- Submodule.mem_of_localization_maximalproof · cited by 4
- MaximalSpectrum.iInf_localization_eq_botproof · cited by 3
- LinearMap.comp_toSpanSingletonproof · cited by 2
- LinearMap.toSpanSingleton_zeroproof · cited by 2
- IsSMulRegular.subsingleton_linearMap_iffproof · cited by 2
- TensorProduct.piScalarRightHom_tmulproof · cited by 2
- Module.Flat.isSMulRegular_of_isRegularproof · cited by 1
- LinearMap.toSpanSingleton_addproof · cited by 1