Mathlib Map

Theorems · Theorem · ring theory

IsSelfAdjoint.star_eq

∀ {R : Type u_1} [inst : Star R] {x : R}, IsSelfAdjoint x → star x = x
Defined in
Mathlib.Algebra.Star.SelfAdjoint
Cited by
58 results in Mathlib
Foundations
Depth 3 from the axioms · uses no axioms
Assumes
Star
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Around this declaration

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

IsSelfAdjoint.sub · cited by 13IsSelfAdjoint.subLE.le.star_eq · cited by 8le.star_eqIsSelfAdjoint.isStarNormal · cited by 8IsSelfAdjoint.isStarNormalIsSelfAdjoint.add · cited by 8IsSelfAdjoint.addIsSelfAdjoint.neg · cited by 7IsSelfAdjoint.negIsSelfAdjoint.smul · cited by 7IsSelfAdjoint.smulIsSelfAdjoint.commute_iff · cited by 5IsSelfAdjoint.commute_iffIsSelfAdjoint.pow · cited by 4IsSelfAdjoint.pownonneg_iff_isSelfAdjoint_and_quasispectrumRestricts · cited by 4nonneg_iff_isSelfAdjoint_…IsStarProjection.le_tfae · cited by 4IsStarProjection.le_tfaeIsSelfAdjoint.conjugate_le_conjugate · cited by 4IsSelfAdjoint.conjugate_l…IsStarProjection.sub_of_mul_eq_left · cited by 3IsStarProjection.sub_of_m…Matrix.IsHermitian.smul · cited by 3IsHermitian.smulIsSelfAdjoint.mul_self_nonneg · cited by 3IsSelfAdjoint.mul_self_no…isSelfAdjoint_iff_isStarNormal_and_quasispectrumRestricts · cited by 2isSelfAdjoint_iff_isStarN…Star.star · cited by 1082Star.starIsSelfAdjoint · cited by 545IsSelfAdjointStar · cited by 496StarIsSelfAdjoint.star_eqCITED BYCITES

Cites3

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

Cited by58

Results whose statement or proof uses this declaration.