Theorems · Theorem · functional analysis
IsSelfAdjoint.mul_self_nonneg
∀ {R : Type u_1} [inst : NonUnitalSemiring R] [inst_1 : PartialOrder R] [inst_2 : StarRing R] [StarOrderedRing R]
{a : R}, IsSelfAdjoint a → 0 ≤ a * a- Defined in
- Mathlib.Algebra.Order.Star.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 20 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- PartialOrderstatement and proof · cited by 6,410
- StarRingstatement and proof · cited by 1,686
- StarOrderedRingstatement and proof · cited by 587
- IsSelfAdjointstatement and proof · cited by 545
- NonUnitalSemiringstatement and proof · cited by 339
- IsSelfAdjoint.star_eqproof · cited by 58
- star_mul_self_nonnegproof · cited by 17
Cited by3
Results whose statement or proof uses this declaration.
- IsStarProjection.nonnegproof · cited by 6
- CFC.abs_eq_cfcₙ_normproof · cited by 2
- IsSelfAdjoint.sq_nonnegproof · cited by 1