Theorems · Theorem · functional analysis
LinearMap.adjoint_toSpanSingleton
∀ {𝕜 : Type u_1} {E : Type u_2} [inst : RCLike 𝕜] [inst_1 : NormedAddCommGroup E] [inst_2 : InnerProductSpace 𝕜 E]
[inst_3 : FiniteDimensional 𝕜 E] (x : E), LinearMap.adjoint (LinearMap.toSpanSingleton 𝕜 E x) = (innerₛₗ 𝕜) x- Cited by
- 1 results in Mathlib
- Foundations
- Depth 196 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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
- RingHom.idstatement · cited by 18,349
- NormedAddCommGroupstatement and proof · cited by 15,752
- LinearMapstatement · cited by 10,215
- InnerProductSpacestatement and proof · cited by 3,523
- LinearEquivstatement · cited by 3,317
- RCLikestatement and proof · cited by 2,829
- FiniteDimensionalstatement and proof · cited by 1,854
- starRingEndstatement · cited by 671
- LinearMap.toSpanSingletonstatement · cited by 78
- LinearMap.adjointstatement and proof · cited by 64
- innerₛₗstatement and proof · cited by 28
Cited by1
Results whose statement or proof uses this declaration.
- Pi.counit_eq_adjointproof · cited by 0