Theorems · Theorem · linear algebra
Matrix.posSemidef_vecMulVec_self_star
∀ {n : Type u_2} {R : Type u_3} [inst : Ring R] [inst_1 : PartialOrder R] [inst_2 : StarRing R] [Finite n]
[StarOrderedRing R] (a : n → R), (Matrix.vecMulVec a (star a)).PosSemidefThe matrix vecMulVec a (star a) is always positive semi-definite.
- Defined in
- Mathlib.LinearAlgebra.Matrix.PosDef
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound
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- AddCommMonoidproof · cited by 12,281
- Ringstatement and proof · cited by 7,463
- PartialOrderstatement and proof · cited by 6,410
- Finitestatement and proof · cited by 3,029
- StarRingstatement and proof · cited by 1,686
- Star.starstatement and proof · cited by 1,082
- StarOrderedRingstatement and proof · cited by 587
- Matrix.PosSemidefstatement and proof · cited by 76
- Matrix.vecMulVecstatement · cited by 52
- Matrix.replicateColproof · cited by 42
- Matrix.vecMulVec_eqproof · cited by 7
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