liftLinear_comp_singleLinearMap — Mathlib

English

The matrix unit with a in position (i, j) equals the vecMulVec of Pi.single i 1 and Pi.single j 1.

Русский

Единичный элемент в позиции (i, j) равен vecMulVec (Pi.single i 1) и (Pi.single j 1).

LaTeX

$$$ \mathrm{single}_{i j} 1 = \mathrm{vecMulVec} (\Pi.single i 1) (\Pi.single j 1) $$$

Lean4

@[simp]
theorem liftLinear_comp_singleLinearMap (f : m → n → α →ₗ[R] β) (i : m) (j : n) :
    liftLinear S f ∘ₗ Matrix.singleLinearMap _ i j = f i j :=
  LinearMap.ext <| liftLinear_single S f i j

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