Theorems · Theorem · linear algebra
Matrix.IsHermitian.im_star_dotProduct_mulVec_self
∀ {𝕜 : Type u_1} {n : Type u_3} {A : Matrix n n 𝕜} [inst : RCLike 𝕜] [inst_1 : Fintype n],
A.IsHermitian → ∀ (x : n → 𝕜), RCLike.im (star x ⬝ᵥ A.mulVec x) = 0- Defined in
- Mathlib.Analysis.Matrix.Hermitian
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 234 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
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
- Realstatement · cited by 25,697
- Fintypestatement and proof · cited by 7,736
- Matrixstatement and proof · cited by 4,303
- AddMonoidHomstatement · cited by 3,230
- RCLikestatement and proof · cited by 2,829
- Star.starstatement and proof · cited by 1,082
- AddMonoid.toZerostatement · cited by 325
- Matrix.mulVecstatement and proof · cited by 267
- dotProductstatement · cited by 194
- RCLike.imstatement and proof · cited by 161
- Matrix.IsHermitianstatement and proof · cited by 126
Cited by1
Results whose statement or proof uses this declaration.
- Matrix.isPositive_toEuclideanLin_iffproof · cited by 2