Theorems · Definition · number theory

QuadraticMap.IsometryEquiv.prodComm

{R : Type u_2} →
  {M₁ : Type u_3} →
    {M₂ : Type u_4} →
      {P : Type u_7} →
        [inst : CommSemiring R] →
          [inst_1 : AddCommMonoid M₁] →
            [inst_2 : AddCommMonoid M₂] →
              [inst_3 : AddCommMonoid P] →
                [inst_4 : Module R M₁] →
                  [inst_5 : Module R M₂] →
                    [inst_6 : Module R P] →
                      (Q₁ : QuadraticMap R M₁ P) → (Q₂ : QuadraticMap R M₂ P) → (Q₁.prod Q₂).IsometryEquiv (Q₂.prod Q₁)

LinearEquiv.prodComm is isometric.

Defined in

Mathlib.LinearAlgebra.QuadraticForm.Prod

Cited by

2 results in Mathlib

Foundations

Depth 43 from the axioms · uses propext, Quot.sound

Assumes

CommSemiringAddCommMonoidAddCommMonoidAddCommMonoidModuleModuleModule