Theorems · Theorem · functional analysis
Matrix.IsHermitian.cfc_eq
∀ {n : Type u_1} {𝕜 : Type u_2} [inst : RCLike 𝕜] [inst_1 : Fintype n] [inst_2 : DecidableEq n] {A : Matrix n n 𝕜}
(hA : A.IsHermitian) (f : ℝ → ℝ), cfc f A = hA.cfc f- Cited by
- 3 results in Mathlib
- Foundations
- Depth 265 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- RCLikeFintypeDecidableEq
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites30
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 and proof · cited by 25,697
- Fintypestatement and proof · cited by 7,736
- Set.Elemproof · cited by 7,166
- Matrixstatement and proof · cited by 4,303
- RCLikestatement and proof · cited by 2,829
- ContinuousMapproof · cited by 2,491
- IsSelfAdjointstatement and proof · cited by 545
- spectrumproof · cited by 510
- Set.domRestrictproof · cited by 383
- RCLike.ofRealproof · cited by 350
- Matrix.diagonalproof · cited by 314
Cited by3
Results whose statement or proof uses this declaration.
- Matrix.PosSemidef.det_sqrtproof · cited by 0
- Matrix.IsHermitian.det_absproof · cited by 0
- Matrix.IsHermitian.charpoly_cfc_eqproof · cited by 0