Theorems · Theorem · operator theory
LinearMap.IsPositive.trace_nonneg
∀ {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.IsPositive → 0 ≤ (LinearMap.trace 𝕜 E) f- Cited by
- 0 results in Mathlib
- Foundations
- Depth 241 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites20
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
- Finsetproof · cited by 13,712
- LinearMapstatement and proof · cited by 10,215
- Fintypeproof · cited by 7,736
- InnerProductSpacestatement and proof · cited by 3,523
- RCLikestatement and proof · cited by 2,829
- FiniteDimensionalproof · cited by 1,854
- Module.Basisproof · cited by 1,477
- Nonempty.someproof · cited by 340
- RCLike.toPartialOrderstatement · cited by 106
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