Theorems · Theorem · operator theory
LinearMap.IsSymmetric.isSymmetric_smul_iff
∀ {𝕜 : Type u_1} {E : Type u_2} [inst : RCLike 𝕜] [inst_1 : NormedAddCommGroup E] [inst_2 : InnerProductSpace 𝕜 E]
{f : E →ₗ[𝕜] E}, f.IsSymmetric → f ≠ 0 → ∀ {α : 𝕜}, (α • f).IsSymmetric ↔ IsSelfAdjoint α- Cited by
- 0 results in Mathlib
- Foundations
- Depth 172 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites16
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
- NormedAddCommGroupstatement and proof · cited by 15,752
- LinearMapstatement and proof · cited by 10,215
- InnerProductSpacestatement and proof · cited by 3,523
- RCLikestatement and proof · cited by 2,829
- Inner.innerproof · cited by 1,089
- starRingEndproof · cited by 671
- IsSelfAdjointstatement · cited by 545
- LinearMap.IsSymmetricstatement and proof · cited by 121
- inner_smul_rightproof · cited by 68
- inner_smul_leftproof · cited by 49
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