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Theorems · Theorem · linear algebra

Matrix.IsHermitian.add

∀ {α : Type u_1} {n : Type u_4} [inst : AddMonoid α] [inst_1 : StarAddMonoid α] {A B : Matrix n n α},
  A.IsHermitian → B.IsHermitian → (A + B).IsHermitian
Defined in
Mathlib.LinearAlgebra.Matrix.Hermitian
Cited by
3 results in Mathlib
Foundations
Depth 19 from the axioms · uses propext, Quot.sound
Assumes
AddMonoidStarAddMonoid
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Matrix.IsHermitian.fromBlocks₁₁ · cited by 2IsHermitian.fromBlocks₁₁Matrix.PosDef.add_posSemidef · cited by 2PosDef.add_posSemidefMatrix.PosSemidef.add · cited by 0PosSemidef.addMatrix · cited by 4303MatrixAddMonoid · cited by 2864AddMonoidStarAddMonoid · cited by 296StarAddMonoidMatrix.IsHermitian · cited by 126Matrix.IsHermitianIsSelfAdjoint.add · cited by 8IsSelfAdjoint.addIsHermitian.addCITED BYCITES

Cites5

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by3

Results whose statement or proof uses this declaration.