Theorems · Theorem · operator theory
Matrix.isPositive_toEuclideanLin_iff
∀ {𝕜 : Type u_1} [inst : RCLike 𝕜] {n : Type u_4} [inst_1 : Fintype n] [inst_2 : DecidableEq n] {A : Matrix n n 𝕜},
(Matrix.toEuclideanLin A).IsPositive ↔ A.PosSemidefA.toEuclideanLin is positive if and only if A is positive semi-definite.
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 235 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.
Cites30
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- RingHom.idstatement · cited by 18,349
- LinearMapstatement · cited by 10,215
- ENNRealstatement · cited by 9,879
- Fintypestatement and proof · cited by 7,736
- Matrixstatement and proof · cited by 4,303
- LinearEquivstatement · cited by 3,317
- RCLikestatement and proof · cited by 2,829
- Inner.innerproof · cited by 1,089
- Star.starproof · cited by 1,082
- WithLp.ofLpproof · cited by 323
- RCLike.reproof · cited by 319
Cited by2
Results whose statement or proof uses this declaration.
- LinearMap.posSemidef_toMatrix_iffproof · cited by 1
- Matrix.posSemidef_iff_eq_sum_vecMulVecproof · cited by 0