Theorems · Theorem · ring theory
skewAdjoint.mem_iff
∀ {R : Type u_1} [inst : AddCommGroup R] [inst_1 : StarAddMonoid R] {x : R}, x ∈ skewAdjoint R ↔ star x = -x- Defined in
- Mathlib.Algebra.Star.SelfAdjoint
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 22 from the axioms · uses propext, Quot.sound
- Assumes
- AddCommGroupStarAddMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddCommGroupstatement and proof · cited by 12,871
- AddSubgroupstatement · cited by 3,232
- Star.starstatement and proof · cited by 1,082
- StarAddMonoidstatement and proof · cited by 296
- skewAdjointstatement · cited by 34
- AddSubgroup.mem_carrierproof · cited by 3
Cited by4
Results whose statement or proof uses this declaration.
- NormedSpace.exp_mem_unitary_of_mem_skewAdjointproof · cited by 1
- skewAdjoint.conjugateproof · cited by 0
- skewAdjoint.conjugate'proof · cited by 0
- skewAdjoint.smul_memproof · cited by 0