Theorems · Theorem · functional analysis
star_left_conjugate_nonneg
∀ {R : Type u_1} [inst : NonUnitalSemiring R] [inst_1 : PartialOrder R] [inst_2 : StarRing R] [StarOrderedRing R]
{a : R}, 0 ≤ a → ∀ (c : R), 0 ≤ star c * a * c- Defined in
- Mathlib.Algebra.Order.Star.Basic
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
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
- Set.rangeproof · cited by 4,705
- add_zeroproof · cited by 2,707
- MulZeroClass.mul_zeroproof · cited by 2,091
- le_reflproof · cited by 2,061
- StarRingstatement and proof · cited by 1,686
- mul_assocproof · cited by 1,667
- MulZeroClass.zero_mulproof · cited by 1,625
- Star.starstatement and proof · cited by 1,082
- add_le_addproof · cited by 666
- StarOrderedRingstatement and proof · cited by 587
- mul_addproof · cited by 413
Cited by6
Results whose statement or proof uses this declaration.
- star_left_conjugate_le_conjugateproof · cited by 6
- Matrix.PosDef.diagonalproof · cited by 4
- star_right_conjugate_nonnegproof · cited by 2
- IsStarProjection.mul_right_and_mul_left_of_nonneg_of_leproof · cited by 1
- Matrix.PosSemidef.diagonalproof · cited by 1
- CStarAlgebra.nnnorm_sub_mul_self_leproof · cited by 1