Theorems · Theorem · linear algebra
Matrix.posSemidef_iff_isHermitian_and_spectrum_nonneg
∀ {𝕜 : Type u_1} {n : Type u_2} [inst : RCLike 𝕜] [inst_1 : Fintype n] [inst_2 : DecidableEq n] {A : Matrix n n 𝕜},
A.PosSemidef ↔ A.IsHermitian ∧ spectrum 𝕜 A ⊆ {a | 0 ≤ a}- Defined in
- Mathlib.Analysis.Matrix.Order
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 264 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- RCLikeFintypeDecidableEq
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- Setstatement · cited by 53,352
- Realproof · cited by 25,697
- Fintypestatement and proof · cited by 7,736
- Set.ofPredstatement and proof · cited by 6,101
- Set.rangeproof · cited by 4,705
- Matrixstatement and proof · cited by 4,303
- RCLikestatement and proof · cited by 2,829
- Nat.cast_zeroproof · cited by 1,870
- spectrumstatement and proof · cited by 510
- RCLike.ofRealproof · cited by 350
- Matrix.IsHermitianstatement and proof · cited by 126
- RCLike.toPartialOrderstatement · cited by 106
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