Theorems · Theorem · functional analysis
LinearMap.adjoint_rTensor
∀ {𝕜 : Type u_1} {E : Type u_2} {F : Type u_3} {G : Type u_4} [inst : RCLike 𝕜] [inst_1 : NormedAddCommGroup E]
[inst_2 : InnerProductSpace 𝕜 E] [inst_3 : NormedAddCommGroup F] [inst_4 : InnerProductSpace 𝕜 F]
[inst_5 : NormedAddCommGroup G] [inst_6 : InnerProductSpace 𝕜 G] [inst_7 : FiniteDimensional 𝕜 E]
[inst_8 : FiniteDimensional 𝕜 F] [inst_9 : FiniteDimensional 𝕜 G] (f : E →ₗ[𝕜] F),
LinearMap.adjoint (LinearMap.rTensor G f) = LinearMap.rTensor G (LinearMap.adjoint f)- Cited by
- 0 results in Mathlib
- Foundations
- Depth 247 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites16
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
- InnerProductSpacestatement and proof · cited by 3,523
- LinearEquivstatement · cited by 3,317
- RCLikestatement and proof · cited by 2,829
- TensorProductstatement · cited by 2,545
- FiniteDimensionalstatement and proof · cited by 1,854
- starRingEndstatement · cited by 671
- LinearMap.idproof · cited by 625
- LinearMap.rTensorstatement · cited by 266
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