liftLinear_apply — Mathlib

English

For any f and matrix M, liftLinear S f evaluated at M equals the double sum over i and j of f(i, j) applied to M(i, j).

Русский

Для любого f и матрицы M применение liftLinear S f к M даёт двойную сумму по i и j от f(i, j) applying к элементу M(i, j).

LaTeX

$$$ liftLinear S f\, M = \sum_{i} \sum_{j} f(i,j)(M_{i j}) $$$

Lean4

theorem liftLinear_apply (f : m → n → α →ₗ[R] β) (M : Matrix m n α) : liftLinear S f M = ∑ i, ∑ j, f i j (M i j) := by
  simp [liftLinear, map_sum, LinearEquiv.congrLeft]

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