Theorems · Theorem · linear algebra
LinearMap.BilinForm.isPosSemidef_def
∀ {R : Type u_1} {M : Type u_2} [inst : CommSemiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]
{B : LinearMap.BilinForm R M} [inst_3 : LE R], B.IsPosSemidef ↔ B.IsSymm ∧ B.IsNonneg- Cited by
- 2 results in Mathlib
- Foundations
- Depth 36 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Modulestatement and proof · cited by 20,661
- AddCommMonoidstatement and proof · cited by 12,281
- CommSemiringstatement and proof · cited by 10,911
- LinearMap.BilinFormstatement and proof · cited by 501
- LinearMap.BilinForm.IsSymmstatement and proof · cited by 35
- LinearMap.BilinForm.IsPosSemidefstatement and proof · cited by 13
- LinearMap.BilinForm.IsNonnegstatement and proof · cited by 8
- LinearMap.BilinForm.IsPosSemidef.isSymmproof · cited by 6
- LinearMap.BilinForm.IsPosSemidef.isNonnegproof · cited by 5
Cited by2
Results whose statement or proof uses this declaration.
- LinearMap.BilinForm.isPosSemidef_iffproof · cited by 3
- LinearMap.BilinForm.IsPosSemidef.smulproof · cited by 0