Theorems · Theorem · linear algebra
Matrix.PosSemidef.nonneg
∀ {𝕜 : Type u_1} {n : Type u_2} [inst : RCLike 𝕜] {A : Matrix n n 𝕜}, A.PosSemidef → 0 ≤ AAlias of the reverse direction of Matrix.nonneg_iff_posSemidef.
- Defined in
- Mathlib.Analysis.Matrix.Order
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 168 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- RCLike
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.
- Matrixstatement and proof · cited by 4,303
- RCLikestatement and proof · cited by 2,829
- RCLike.toPartialOrderstatement · cited by 106
- Matrix.PosSemidefstatement · cited by 76
- Matrix.nonneg_iff_posSemidefproof · cited by 2
Cited by7
Results whose statement or proof uses this declaration.
- ProbabilityTheory.covarianceBilin_multivariateGaussianproof · cited by 3
- Matrix.PosSemidef.posDef_iff_isUnitproof · cited by 3
- Matrix.PosSemidef.kroneckerproof · cited by 2
- Matrix.isStrictlyPositive_iff_posDefproof · cited by 2
- Matrix.PosSemidef.dotProduct_mulVec_zero_iffproof · cited by 1
- Matrix.PosSemidef.inv_sqrtproof · cited by 0
- Matrix.PosSemidef.det_sqrtproof · cited by 0