tensorComm — Mathlib

English

TensorProduct commutes the tensor product of quadratic forms up to a canonical isometry; i.e., tensorComm Q1 Q2 gives an isometry between Q1.tmul Q2 and Q2.tmul Q1.

Русский

TensorProduct commutator для квадратичных форм существует как канонная изометрия между Q1.tmul Q2 и Q2.tmul Q1.

LaTeX

$$$\\text{tensorComm} (Q_1) (Q_2): (Q_1.tmul Q_2) \\IsometryEquiv (Q_2.tmul Q_1)$$$

Lean4

/-- `TensorProduct.comm` preserves tensor products of quadratic forms. -/
@[simps toLinearEquiv]
def tensorComm (Q₁ : QuadraticForm R M₁) (Q₂ : QuadraticForm R M₂) : (Q₁.tmul Q₂).IsometryEquiv (Q₂.tmul Q₁)
    where
  toLinearEquiv := TensorProduct.comm R M₁ M₂
  map_app' := tmul_tensorComm_apply Q₁ Q₂

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