Theorems · Theorem · functional analysis
LinearMap.range_self_comp_adjoint
∀ {𝕜 : Type u_1} {E : Type u_2} {F : Type u_3} [inst : RCLike 𝕜] [inst_1 : NormedAddCommGroup E]
[inst_2 : NormedAddCommGroup F] [inst_3 : InnerProductSpace 𝕜 E] [inst_4 : InnerProductSpace 𝕜 F]
[inst_5 : FiniteDimensional 𝕜 E] [inst_6 : FiniteDimensional 𝕜 F] (A : E →ₗ[𝕜] F),
(A ∘ₗ LinearMap.adjoint A).range = A.range- Cited by
- 0 results in Mathlib
- Foundations
- Depth 197 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites17
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 and proof · cited by 18,349
- NormedAddCommGroupstatement and proof · cited by 15,752
- LinearMapstatement and proof · cited by 10,215
- Submodulestatement · cited by 7,192
- 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
- LinearMap.compstatement and proof · cited by 1,642
- LinearMap.rangestatement · cited by 893
- starRingEndstatement · cited by 671
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