Theorems · Theorem · linear algebra
Matrix.PosSemidef.re_dotProduct_nonneg
∀ {n : Type u_2} {𝕜 : Type u_3} [inst : Fintype n] [inst_1 : RCLike 𝕜] {A : Matrix n n 𝕜},
A.PosSemidef → ∀ (x : n → 𝕜), 0 ≤ RCLike.re (star x ⬝ᵥ A.mulVec x)- Defined in
- Mathlib.Analysis.Matrix.PosDef
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 98 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites15
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- Realstatement · cited by 25,697
- Fintypestatement and proof · cited by 7,736
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- AddMonoidHomstatement · cited by 3,230
- RCLikestatement and proof · cited by 2,829
- Star.starstatement · cited by 1,082
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- RCLike.restatement · cited by 319
- Matrix.mulVecstatement · cited by 267
- dotProductstatement · cited by 194
- RCLike.toPartialOrderstatement · cited by 106
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