Mathlib Map

Theorems · Definition · functional analysis

LinearIsometry.id

{R : Type u_1} →
  {E : Type u_5} → [inst : Semiring R] → [inst_1 : SeminormedAddCommGroup E] → [inst_2 : Module R E] → E →ₗᵢ[R] E

The identity linear isometry.

Defined in
Mathlib.Analysis.Normed.Operator.LinearIsometry
Cited by
12 results in Mathlib
Foundations
Depth 22 from the axioms · uses no axioms
Assumes
SemiringSeminormedAddCommGroupModule
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

LinearIsometry.lTensor · cited by 5LinearIsometry.lTensorLinearIsometry.rTensor · cited by 5LinearIsometry.rTensorisConformalMap_id · cited by 2isConformalMap_idLinearMap.normDet_id · cited by 1LinearMap.normDet_idLinearIsometry.one_def · cited by 0LinearIsometry.one_defLinearIsometry.lTensor_def · cited by 0LinearIsometry.lTensor_defLinearIsometry.rTensor_def · cited by 0LinearIsometry.rTensor_defLinearIsometry.coe_id · cited by 0LinearIsometry.coe_idLinearIsometry.id_apply · cited by 0LinearIsometry.id_applyLinearIsometry.id_comp · cited by 0LinearIsometry.id_compLinearIsometry.id_toContinuousLinearMap · cited by 0LinearIsometry.id_toConti…LinearIsometry.id_toLinearMap · cited by 0LinearIsometry.id_toLinea…TensorProduct.mapIsometry_id_id · cited by 0TensorProduct.mapIsometry…LinearIsometry.comp_id · cited by 0LinearIsometry.comp_idModule · cited by 20661ModuleRingHom.id · cited by 18349RingHom.idSemiring · cited by 13802SemiringSeminormedAddCommGroup · cited by 2671SeminormedAddCommGroupLinearMap.id · cited by 625LinearMap.idLinearIsometry · cited by 194LinearIsometryLinearIsometry.idCITED BYCITES

Cites6

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by14

Results whose statement or proof uses this declaration.