Theorems · Theorem · functional analysis
LinearIsometry.coe_toSpanSingleton
∀ {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),
(LinearIsometry.toSpanSingleton 𝕜 E hv).toLinearMap = LinearMap.toSpanSingleton 𝕜 E v- Defined in
- Mathlib.Analysis.Normed.Operator.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 122 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- RingHom.idstatement · cited by 18,349
- NormedSpacestatement and proof · cited by 12,499
- LinearMapstatement · cited by 10,215
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- Norm.normstatement and proof · cited by 5,413
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- LinearMap.toSpanSingletonstatement · cited by 78
- LinearIsometry.toLinearMapstatement · cited by 55
- LinearIsometry.toSpanSingletonstatement · cited by 6
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