Theorems · Theorem · ring theory
IsSelfAdjoint.neg
∀ {R : Type u_1} [inst : AddGroup R] [inst_1 : StarAddMonoid R] {x : R}, IsSelfAdjoint x → IsSelfAdjoint (-x)- Defined in
- Mathlib.Algebra.Star.SelfAdjoint
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 20 from the axioms · uses propext, Quot.sound
- Assumes
- AddGroupStarAddMonoid
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.
- AddGroupstatement and proof · cited by 4,410
- IsSelfAdjointstatement and proof · cited by 545
- StarAddMonoidstatement and proof · cited by 296
- IsSelfAdjoint.star_eqproof · cited by 58
- star_negproof · cited by 8
Cited by8
Results whose statement or proof uses this declaration.
- selfAdjointproof · cited by 135
- CFC.posPart_negproof · cited by 4
- IsSelfAdjoint.norm_sub_eq_maxproof · cited by 1
- CFC.negPart_eq_negproof · cited by 1
- spectrum_star_mul_self_nonnegproof · cited by 1
- Matrix.IsHermitian.negproof · cited by 1
- IsSelfAdjoint.neg_algebraMap_norm_le_selfproof · cited by 0
- CFC.posPart_negPart_uniqueproof · cited by 0