Theorems · Theorem · linear algebra
LinearMap.isPosSemidef_iff_posSemidef_toMatrix
∀ {M : Type u_2} {n : Type u_3} [inst : AddCommMonoid M] [inst_1 : Fintype n] [inst_2 : DecidableEq n] {R : Type u_4}
[inst_3 : CommRing R] [inst_4 : StarRing R] [inst_5 : PartialOrder R] [inst_6 : Module R M] {B : M →ₗ⋆[R] M →ₗ[R] R}
(b : Module.Basis n R M), B.IsPosSemidef ↔ ((LinearMap.toMatrix₂ b b) B).PosSemidef- Cited by
- 0 results in Mathlib
- Foundations
- Depth 92 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites30
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- DFunLike.coestatement and proof · cited by 62,936
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement and proof · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- AddCommMonoidstatement and proof · cited by 12,281
- LinearMapstatement and proof · cited by 10,215
- Fintypestatement and proof · cited by 7,736
- PartialOrderstatement and proof · cited by 6,410
- Matrixstatement · cited by 4,303
- LinearEquivstatement · cited by 3,317
- StarRingstatement and proof · cited by 1,686
- Module.Basisstatement and proof · cited by 1,477
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