Theorems · Definition · number theory

LinearEquiv.congrQuadraticMap

{R : Type u_3} →
  {M : Type u_4} →
    {N : Type u_5} →
      {P : Type u_6} →
        [inst : CommSemiring R] →
          [inst_1 : AddCommMonoid M] →
            [inst_2 : Module R M] →
              [inst_3 : AddCommMonoid N] →
                [inst_4 : Module R N] →
                  [inst_5 : AddCommMonoid P] →
                    [inst_6 : Module R P] → (N ≃ₗ[R] P) → QuadraticMap R M N ≃ₗ[R] QuadraticMap R M P

When N and P are equivalent, quadratic maps on M into N are equivalent to quadratic maps on M into P. See LinearMap.BilinMap.congr₂ for the bilinear map version.

Defined in

Mathlib.LinearAlgebra.QuadraticForm.Basic

Cited by

3 results in Mathlib

Foundations

Depth 53 from the axioms · uses propext, Quot.sound

Assumes

CommSemiringAddCommMonoidModuleAddCommMonoidModuleAddCommMonoidModule