Theorems · Inductive type · number theory

QuadraticMap.Isometry

{R : Type u_1} →
  {M₁ : Type u_3} →
    {M₂ : Type u_4} →
      {N : Type u_7} →
        [inst : CommSemiring R] →
          [inst_1 : AddCommMonoid M₁] →
            [inst_2 : AddCommMonoid M₂] →
              [inst_3 : AddCommMonoid N] →
                [inst_4 : Module R M₁] →
                  [inst_5 : Module R M₂] →
                    [inst_6 : Module R N] → QuadraticMap R M₁ N → QuadraticMap R M₂ N → Type (max u_3 u_4)

An isometry between two quadratic spaces M₁, Q₁ and M₂, Q₂ over a ring R, is a linear map between M₁ and M₂ that commutes with the quadratic forms.

Defined in

Mathlib.LinearAlgebra.QuadraticForm.Isometry

Cited by

69 results in Mathlib

Foundations

Depth 3 from the axioms · uses no axioms

Assumes

CommSemiringAddCommMonoidAddCommMonoidAddCommMonoidModuleModuleModule