tensorLId — Mathlib

English

For Q1 and x in M1 ⊗ R, the tmul of Q1 with sq applied to x equals Q1 applied to rid(x).

Русский

С точностью: Q1 ⊗ sq применимо к x равно Q1( rid(x) ).

LaTeX

$$$(Q_1 \otimes Q_2).\mathrm{tmul} \; (x) = Q_1 x_1 \otimes Q_2 x_2$$$

Lean4

/-- `TensorProduct.lid` preserves tensor products of quadratic forms. -/
@[simps toLinearEquiv]
def tensorLId (Q₂ : QuadraticForm R M₂) : (QuadraticForm.tmul (sq (R := R)) Q₂).IsometryEquiv Q₂
    where
  toLinearEquiv := TensorProduct.lid R M₂
  map_app' := tmul_tensorLId_apply Q₂

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