Theorems · Theorem · linear algebra
Matrix.IsHermitian.rank_eq_rank_diagonal
∀ {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), A.rank = (Matrix.diagonal hA.eigenvalues).rankrank of a Hermitian matrix is the rank of after diagonalization by the eigenvector unitary
- Defined in
- Mathlib.Analysis.Matrix.Spectrum
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 262 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.
Cites21
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- Fintypestatement and proof · cited by 7,736
- Algebra.algebraMapproof · cited by 4,706
- Matrixstatement and proof · cited by 4,303
- RCLikestatement and proof · cited by 2,829
- Fintype.cardproof · cited by 1,386
- Star.starproof · cited by 1,082
- RCLike.ofRealproof · cited by 350
- Matrix.diagonalstatement and proof · cited by 314
- Matrix.IsHermitianstatement and proof · cited by 126
- Fintype.card_congr'proof · cited by 60
- Matrix.rankstatement and proof · cited by 48
Cited by1
Results whose statement or proof uses this declaration.
- Matrix.IsHermitian.rank_eq_card_non_zero_eigsproof · cited by 0