Theorems · Definition · linear algebra
Matrix.IsHermitian
{α : Type u_1} → {n : Type u_4} → [Star α] → Matrix n n α → PropA matrix is Hermitian if it is equal to its conjugate transpose. On the reals, this definition captures symmetric matrices.
- Defined in
- Mathlib.LinearAlgebra.Matrix.Hermitian
- Cited by
- 126 results in Mathlib
- Foundations
- Depth 16 from the axioms, rests on 66 definitions · uses Quot.sound
- Assumes
- Star
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Matrixstatement and proof · cited by 4,303
- Starstatement and proof · cited by 496
- Matrix.conjTransposeproof · cited by 202
Cited by134
Results whose statement or proof uses this declaration.
- Matrix.PosSemidefproof · cited by 76
- Matrix.PosDefproof · cited by 68
- Matrix.IsHermitian.eigenvaluesstatement and proof · cited by 34
- Matrix.IsHermitian.eigenvectorUnitarystatement and proof · cited by 25
- Matrix.IsHermitian.eigenvectorBasisstatement and proof · cited by 12
- Matrix.IsHermitian.eqstatement and proof · cited by 11
- Matrix.IsHermitian.spectral_theoremstatement and proof · cited by 10
- Matrix.PosSemidef.isHermitianstatement · cited by 8
- Matrix.PosSemidef.eigenvalues_nonnegstatement · cited by 6
- Matrix.IsHermitian.cfcAuxstatement and proof · cited by 6
- Matrix.posSemidef_iff_dotProduct_mulVecstatement and proof · cited by 5
- Matrix.PosSemidef.of_dotProduct_mulVec_nonnegstatement and proof · cited by 5