Theorems · Theorem · linear algebra
Matrix.isStrictlyPositive_iff_posDef
∀ {𝕜 : Type u_1} {n : Type u_2} [inst : RCLike 𝕜] [inst_1 : Fintype n] [inst_2 : DecidableEq n] {x : Matrix n n 𝕜},
IsStrictlyPositive x ↔ x.PosDef- Defined in
- Mathlib.Analysis.Matrix.Order
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 267 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- RCLikeFintypeDecidableEq
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Fintypestatement and proof · cited by 7,736
- Matrixstatement and proof · cited by 4,303
- RCLikestatement and proof · cited by 2,829
- RCLike.toPartialOrderstatement · cited by 106
- IsStrictlyPositivestatement and proof · cited by 75
- Matrix.PosDefstatement and proof · cited by 68
- IsStrictlyPositive.nonnegproof · cited by 18
- IsStrictlyPositive.isUnitproof · cited by 12
- Matrix.PosSemidef.nonnegproof · cited by 7
- IsUnit.isStrictlyPositiveproof · cited by 5
- Matrix.PosDef.posSemidefproof · cited by 5
- Matrix.PosDef.isUnitproof · cited by 4
Cited by2
Results whose statement or proof uses this declaration.
- Matrix.PosDef.isStrictlyPositiveproof · cited by 0
- Matrix.IsStrictlyPositive.posDefproof · cited by 0