Theorems · Definition · number theory

QuadraticMap.toBilin

{ι : Type u_1} →
  {R : Type u_2} →
    {M : Type u_3} →
      {N : Type u_4} →
        [LinearOrder ι] →
          [inst : CommRing R] →
            [inst_1 : AddCommGroup M] →
              [inst_2 : AddCommGroup N] →
                [inst_3 : Module R M] →
                  [inst_4 : Module R N] → QuadraticMap R M N → Module.Basis ι R M → LinearMap.BilinMap R M N

Given an ordered basis, produce a bilinear form associated with the quadratic form. Unlike QuadraticMap.associated, this is not symmetric; however, as a result it can be used even in characteristic two. When considered as a matrix, the form is triangular.

Defined in

Mathlib.LinearAlgebra.QuadraticForm.Basis

Cited by

6 results in Mathlib

Foundations

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

Assumes

LinearOrderCommRingAddCommGroupAddCommGroupModuleModule