Theorems · Theorem · functional analysis
LinearIsometry.toSpanSingleton_apply
∀ {𝕜 : Type u_1} {E : Type u_4} [inst : SeminormedAddCommGroup E] [inst_1 : NontriviallyNormedField 𝕜]
[inst_2 : NormedSpace 𝕜 E] {v : E} (hv : ‖v‖ = 1) (a : 𝕜), (LinearIsometry.toSpanSingleton 𝕜 E hv) a = a • v- Defined in
- Mathlib.Analysis.Normed.Operator.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 122 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Realstatement · cited by 25,697
- RingHom.idstatement · cited by 18,349
- NormedSpacestatement and proof · cited by 12,499
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- Norm.normstatement and proof · cited by 5,413
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- LinearIsometrystatement · cited by 194
- LinearIsometry.toSpanSingletonstatement · cited by 6
Cited by1
Results whose statement or proof uses this declaration.
- Orthonormal.linearIsometryEquiv_symm_apply_single_oneproof · cited by 1