Theorems · Definition · linear algebra

LinearMap.SeparatingLeft

{R : Type u_1} →
  {R₁ : Type u_2} →
    {R₂ : Type u_3} →
      {M : Type u_5} →
        {M₁ : Type u_6} →
          {M₂ : Type u_7} →
            [inst : CommSemiring R] →
              [inst_1 : AddCommMonoid M] →
                [inst_2 : Module R M] →
                  [inst_3 : CommSemiring R₁] →
                    [inst_4 : AddCommMonoid M₁] →
                      [inst_5 : Module R₁ M₁] →
                        [inst_6 : CommSemiring R₂] →
                          [inst_7 : AddCommMonoid M₂] →
                            [inst_8 : Module R₂ M₂] →
                              {I₁ : R₁ →+* R} → {I₂ : R₂ →+* R} → (M₁ →ₛₗ[I₁] M₂ →ₛₗ[I₂] M) → Prop

A bilinear map is called left-separating if the only element that is left-orthogonal to every other element is 0; i.e., for every nonzero x in M₁, there exists y in M₂ with B x y ≠ 0.

Defined in

Mathlib.LinearAlgebra.SesquilinearForm.Basic

Cited by

47 results in Mathlib

Foundations

Depth 32 from the axioms · uses propext, Quot.sound

Assumes

CommSemiringAddCommMonoidModuleCommSemiringAddCommMonoidModuleCommSemiringAddCommMonoidModule