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Theorems · Theorem · number theory

QuadraticMap.PosDef.smul

∀ {M : Type u_4} {N : Type u_5} [inst : AddCommMonoid M] [inst_1 : PartialOrder N] [inst_2 : AddCommMonoid N]
  {R : Type u_8} [inst_3 : CommSemiring R] [inst_4 : PartialOrder R] [inst_5 : Module R M] [inst_6 : Module R N]
  [PosSMulStrictMono R N] {Q : QuadraticMap R M N}, Q.PosDef → ∀ {a : R}, 0 < a → (a • Q).PosDef
Defined in
Mathlib.LinearAlgebra.QuadraticForm.Basic
Cited by
0 results in Mathlib
Foundations
Depth 41 from the axioms · uses propext, Quot.sound
Assumes
AddCommMonoidPartialOrderAddCommMonoidCommSemiringPartialOrderModuleModulePosSMulStrictMono
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Module · cited by 20661ModuleAddCommMonoid · cited by 12281AddCommMonoidCommSemiring · cited by 10911CommSemiringPartialOrder · cited by 6410PartialOrderQuadraticMap · cited by 262QuadraticMapPosSMulStrictMono · cited by 128PosSMulStrictMonoQuadraticMap.PosDef · cited by 31QuadraticMap.PosDefsmul_pos · cited by 5smul_posPosDef.smulCITED BYCITES

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