Theorems · Theorem · number theory

QuadraticMap.IsometryEquiv.map_posDef_iff

∀ {R : Type u_1} {M : Type u_2} {M' : Type u_3} [inst : AddCommGroup M] [inst_1 : AddCommGroup M'] [inst_2 : CommRing R]
  [inst_3 : LinearOrder R] [inst_4 : Module R M] {Q : QuadraticForm R M} [inst_5 : Module R M']
  {Q' : QuadraticForm R M'} {V : Submodule R M} (e : QuadraticMap.IsometryEquiv Q Q'),
  (QuadraticMap.restrict Q' (Submodule.map (↑e.toLinearEquiv) V)).PosDef ↔ (QuadraticMap.restrict Q V).PosDef

Defined in

Mathlib.LinearAlgebra.QuadraticForm.Signature

Cited by

1 results in Mathlib

Foundations

Depth 44 from the axioms · uses propext, Quot.sound

Assumes

AddCommGroupAddCommGroupCommRingLinearOrderModuleModule