Theorems · Theorem · linear algebra
Matrix.IsHermitian.eigenvectorUnitary_mulVec
∀ {𝕜 : Type u_1} [inst : RCLike 𝕜] {n : Type u_2} [inst_1 : Fintype n] {A : Matrix n n 𝕜} [inst_2 : DecidableEq n]
(hA : A.IsHermitian) (j : n), (↑hA.eigenvectorUnitary).mulVec (Pi.single j 1) = (hA.eigenvectorBasis j).ofLp- Defined in
- Mathlib.Analysis.Matrix.Spectrum
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 258 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.
Cites16
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
- ENNRealstatement · cited by 9,879
- Fintypestatement and proof · cited by 7,736
- Matrixstatement and proof · cited by 4,303
- Submonoidstatement · cited by 3,086
- RCLikestatement and proof · cited by 2,829
- Pi.singlestatement · cited by 518
- WithLp.ofLpstatement and proof · cited by 323
- EuclideanSpacestatement · cited by 307
- Matrix.mulVecstatement · cited by 267
- OrthonormalBasisstatement · cited by 188
- Matrix.IsHermitianstatement and proof · cited by 126
Cited by2
Results whose statement or proof uses this declaration.
- Matrix.IsHermitian.star_eigenvectorUnitary_mulVecproof · cited by 1
- Matrix.IsHermitian.conjStarAlgAut_star_eigenvectorUnitaryproof · cited by 1