Theorems · Theorem · operator theory
LinearMap.IsSymmetric.splits_charpoly
∀ {𝕜 : Type u_1} [inst : RCLike 𝕜] {E : Type u_2} [inst_1 : NormedAddCommGroup E] [inst_2 : InnerProductSpace 𝕜 E]
{T : E →ₗ[𝕜] E} [inst_3 : FiniteDimensional 𝕜 E], T.IsSymmetric → T.charpoly.Splits- Cited by
- 2 results in Mathlib
- Foundations
- Depth 260 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- 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
- Finset.univproof · cited by 3,473
- RCLikestatement and proof · cited by 2,829
- FiniteDimensionalstatement and proof · cited by 1,854
- Module.finrankproof · cited by 1,770
- Finset.valproof · cited by 438
- Multiset.cardproof · cited by 375
- RCLike.ofRealproof · cited by 350
- Polynomial.Splitsstatement · cited by 290
Cited by2
Results whose statement or proof uses this declaration.
- LinearMap.IsSymmetric.trace_eq_sum_eigenvaluesproof · cited by 1
- LinearMap.IsSymmetric.det_eq_prod_eigenvaluesproof · cited by 1