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Theorems · Theorem · linear algebra

Matrix.isHermitian_diagonal

∀ {α : Type u_1} {n : Type u_4} [inst : AddMonoid α] [inst_1 : StarAddMonoid α] [TrivialStar α] [inst_3 : DecidableEq n]
  (v : n → α), (Matrix.diagonal v).IsHermitian

A diagonal matrix is Hermitian if the entries have the trivial star operation (such as on the reals).

Defined in
Mathlib.LinearAlgebra.Matrix.Hermitian
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Foundations
Depth 22 from the axioms · uses propext, Quot.sound
Assumes
AddMonoidStarAddMonoidTrivialStarDecidableEq
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AddMonoid · cited by 2864AddMonoidMatrix.diagonal · cited by 314Matrix.diagonalStarAddMonoid · cited by 296StarAddMonoidMatrix.IsHermitian · cited by 126Matrix.IsHermitianTrivialStar · cited by 66TrivialStarIsSelfAdjoint.all · cited by 5IsSelfAdjoint.allMatrix.isHermitian_diagonal_of_self_adjoint · cited by 3Matrix.isHermitian_diagon…Matrix.isHermitian_diagonalCITED BYCITES

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