Theorems · Theorem · operator theory
LinearMap.IsPositive.nonneg_eigenvalues
∀ {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} {n : ℕ} (hT : T.IsPositive) (hn : Module.finrank 𝕜 E = n)
(i : Fin n), 0 ≤ ⋯.eigenvalues hn i- Cited by
- 3 results in Mathlib
- Foundations
- Depth 258 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites22
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Realstatement · cited by 25,697
- RingHom.idstatement and proof · cited by 18,349
- NormedAddCommGroupstatement and proof · cited by 15,752
- LinearMapstatement and proof · cited by 10,215
- mul_oneproof · cited by 3,885
- InnerProductSpacestatement and proof · cited by 3,523
- RCLikestatement and proof · cited by 2,829
- FiniteDimensionalstatement and proof · cited by 1,854
- Module.finrankstatement and proof · cited by 1,770
- Inner.innerproof · cited by 1,089
- one_powproof · cited by 521
Cited by3
Results whose statement or proof uses this declaration.
- LinearMap.sq_singularValues_finproof · cited by 4
- ContinuousLinearMap.isPositive_iff_eq_sum_rankOneproof · cited by 1
- LinearMap.card_support_singularValuesproof · cited by 0