Theorems · Theorem · functional analysis
LinearMap.isSymmetric_adjoint_mul_self
∀ {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] (T : E →ₗ[𝕜] E), (LinearMap.adjoint T * T).IsSymmetricThe Gram operator T†T is symmetric. See LinearMap.isSymmetric_adjoint_comp_self for a version
where the domain and codomain are distinct.
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- 0 results in Mathlib
- Foundations
- Depth 195 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites14
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
- FiniteDimensionalstatement and proof · cited by 1,854
- Inner.innerproof · cited by 1,089
- starRingEndstatement · cited by 671
- LinearMap.IsSymmetricstatement · cited by 121
- LinearMap.adjointstatement · cited by 64
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