Theorems · Definition · linear algebra

LinearMap.BilinForm.tmul

{R : Type uR} →
  {A : Type uA} →
    {M₁ : Type uM₁} →
      {M₂ : Type uM₂} →
        [inst : CommSemiring R] →
          [inst_1 : CommSemiring A] →
            [inst_2 : AddCommMonoid M₁] →
              [inst_3 : AddCommMonoid M₂] →
                [inst_4 : Algebra R A] →
                  [inst_5 : Module R M₁] →
                    [inst_6 : Module A M₁] →
                      [inst_7 : SMulCommClass R A M₁] →
                        [IsScalarTower R A M₁] →
                          [inst_9 : Module R M₂] →
                            LinearMap.BilinForm A M₁ →
                              LinearMap.BilinMap R M₂ R → LinearMap.BilinMap A (TensorProduct R M₁ M₂) A

The tensor product of two bilinear forms, a shorthand for dot notation.

Defined in

Mathlib.LinearAlgebra.BilinearForm.TensorProduct

Cited by

9 results in Mathlib

Foundations

Depth 79 from the axioms · uses propext, Quot.sound

Assumes

CommSemiringCommSemiringAddCommMonoidAddCommMonoidAlgebraModuleModuleSMulCommClassIsScalarTowerModule