Theorems · Theorem · linear algebra
Matrix.PosSemidef.det_nonneg
∀ {n : Type u_2} {𝕜 : Type u_3} [inst : Fintype n] [inst_1 : RCLike 𝕜] {A : Matrix n n 𝕜} [inst_2 : DecidableEq n],
A.PosSemidef → 0 ≤ A.det- Defined in
- Mathlib.Analysis.Matrix.PosDef
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 266 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- FintypeRCLikeDecidableEq
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- Finset.univproof · cited by 3,473
- RCLikestatement and proof · cited by 2,829
- Matrix.detstatement · cited by 665
- RCLike.toPartialOrderstatement · cited by 106
- Matrix.PosSemidefstatement and proof · cited by 76
- Finset.prod_nonnegproof · cited by 39
- Matrix.PosSemidef.isHermitianproof · cited by 8
- Matrix.PosSemidef.eigenvalues_nonnegproof · cited by 6
- Matrix.IsHermitian.det_eq_prod_eigenvaluesproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- Matrix.PosSemidef.det_sqrtproof · cited by 0