Theorems · Theorem · operator theory
LinearMap.isSymmetric_linearIsometryEquiv_conj_iff
∀ {𝕜 : Type u_1} {E : Type u_2} [inst : RCLike 𝕜] [inst_1 : SeminormedAddCommGroup E] [inst_2 : InnerProductSpace 𝕜 E]
{F : Type u_3} [inst_3 : SeminormedAddCommGroup F] [inst_4 : InnerProductSpace 𝕜 F] (T : E →ₗ[𝕜] E) (f : E ≃ₗᵢ[𝕜] F),
(↑f.toLinearEquiv ∘ₗ T ∘ₗ ↑f.symm.toLinearEquiv).IsSymmetric ↔ T.IsSymmetric- Cited by
- 0 results in Mathlib
- Foundations
- Depth 169 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- RingHom.idstatement and proof · cited by 18,349
- LinearMapstatement and proof · cited by 10,215
- InnerProductSpacestatement and proof · cited by 3,523
- RCLikestatement and proof · cited by 2,829
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- LinearMap.compstatement and proof · cited by 1,642
- LinearEquiv.toLinearMapstatement and proof · cited by 1,171
- Inner.innerproof · cited by 1,089
- LinearIsometryEquivstatement and proof · cited by 748
- LinearIsometryEquiv.symmstatement and proof · cited by 287
- LinearMap.IsSymmetricstatement and proof · cited by 121
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