English
Similar to 133115, but stated for the weighted sum squares isometry framed in a different context.
Русский
Аналогично 133115, но с другой формулировкой для взвешенной суммы квадратов.
LaTeX
$$$\exists w: Fin(\mathrm{finrank}) \to K, Q \text{ Equivalent } \operatorname{weightedSumSquares} K w$$$
Lean4
/-- `LinearMap.inr` as an isometry. -/
@[simps!]
def inr (Q₁ : QuadraticMap R M₁ P) (Q₂ : QuadraticMap R M₂ P) : Q₂ →qᵢ (Q₁.prod Q₂)
where
toLinearMap := LinearMap.inr R _ _
map_app' m₁ := by simp