Theorems · Theorem · number theory

QuadraticMap.nondegenerate_associated_iff

∀ {R : Type u_1} {M : Type u_2} {P : Type u_4} [inst : AddCommGroup M] [inst_1 : AddCommGroup P] [inst_2 : CommRing R]
  [inst_3 : Module R M] [inst_4 : Module R P] {Q : QuadraticMap R M P} [inst_5 : Invertible 2],
  LinearMap.Nondegenerate (QuadraticMap.associated Q) ↔ QuadraticMap.Nondegenerate

If 2 is invertible in the coefficient ring, a quadratic map is nondegenerate iff its associated bilinear map is nondegenerate.

Defined in

Mathlib.LinearAlgebra.QuadraticForm.Radical

Cited by

0 results in Mathlib

Foundations

Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddCommGroupAddCommGroupCommRingModuleModuleInvertible