Theorems · Theorem · ring theory
IsSelfAdjoint.add
∀ {R : Type u_1} [inst : AddMonoid R] [inst_1 : StarAddMonoid R] {x y : R},
IsSelfAdjoint x → IsSelfAdjoint y → IsSelfAdjoint (x + y)- Defined in
- Mathlib.Algebra.Star.SelfAdjoint
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses propext
- Assumes
- AddMonoidStarAddMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddMonoidstatement and proof · cited by 2,864
- IsSelfAdjointstatement and proof · cited by 545
- StarAddMonoidstatement and proof · cited by 296
- IsSelfAdjoint.star_eqproof · cited by 58
- StarAddMonoid.star_addproof · cited by 29
Cited by8
Results whose statement or proof uses this declaration.
- Matrix.IsHermitian.addproof · cited by 3
- SpectrumRestricts.nnreal_addproof · cited by 2
- Unitization.convexOn_of_convexOn_inr_compproof · cited by 1
- CStarAlgebra.spectralOrderedRingproof · cited by 1
- spectrum_star_mul_self_nonnegproof · cited by 1
- IsStarProjection.addproof · cited by 0
- IsStarProjection.add_sub_mul_of_commuteproof · cited by 0
- Unitization.concaveOn_of_concaveOn_inr_compproof · cited by 0