Theorems · Theorem · number theory
QuadraticForm.equivalent_of_isAlgClosed
∀ {K : Type u_2} [inst : Field K] [IsAlgClosed K] [inst_2 : Invertible 2] {M : Type u_3} [inst_3 : AddCommGroup M]
[inst_4 : Module K M] [FiniteDimensional K M] (Q₁ Q₂ : QuadraticForm K M),
LinearMap.SeparatingLeft (QuadraticMap.associated Q₁) →
LinearMap.SeparatingLeft (QuadraticMap.associated Q₂) → QuadraticMap.Equivalent Q₁ Q₂All nondegenerate quadratic forms on an algebraically closed field of characteristic not equal to 2 are equivalent.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 123 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement · cited by 18,349
- AddCommGroupstatement and proof · cited by 12,871
- LinearMapstatement · cited by 10,215
- Fieldstatement and proof · cited by 7,404
- FiniteDimensionalstatement and proof · cited by 1,854
- Invertiblestatement and proof · cited by 549
- QuadraticFormstatement and proof · cited by 507
- QuadraticMapstatement · cited by 262
- IsAlgClosedstatement and proof · cited by 150
- LinearMap.BilinMapstatement · cited by 85
Cited by1
Results whose statement or proof uses this declaration.
- QuadraticForm.complex_equivalentproof · cited by 0