Theorems · Theorem · linear algebra
Matrix.IsStrictlyPositive.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.PosDefAlias of the forward direction of Matrix.isStrictlyPositive_iff_posDef.
- Defined in
- Mathlib.Analysis.Matrix.Order
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 268 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.
Cites7
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 · cited by 75
- Matrix.PosDefstatement · cited by 68
- Matrix.isStrictlyPositive_iff_posDefproof · cited by 2
Cited by0
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