fst — Mathlib

English

There exists weights w such that Q is equivalent to the weighted sum-of-squares representation; a standard diagonalization result.

Русский

Существуют веса w, делающие Q эквивалентной диагонализированной форме весов.

LaTeX

$$$\exists w, Q \text{ Equivalent } \operatorname{weightedSumSquares} K w$$$

Lean4

/-- `LinearMap.fst` as an isometry, when the second space has the zero quadratic form. -/
@[simps!]
def fst (Q₁ : QuadraticMap R M₁ P) : (Q₁.prod (0 : QuadraticMap R M₂ P)) →qᵢ Q₁
    where
  toLinearMap := LinearMap.fst R _ _
  map_app' m₁ := by simp

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