ofLinearEquiv — Mathlib

English

There is a linear equivalence between the space of matrices M_n(α) viewed as functions m → n → α and the space of matrices; i.e., (m → n → α) ≃_ℓ[R] Matrix m n α.

Русский

Существует линейное эквалентное соответствие между пространством матриц M_n(α) и пространством функций, задаваемых парой индексов: (m → n → α) ≃_ℓ[R] Matrix m n α.

LaTeX

$$$(m \\to n \\to α) \\simeq_ℓ[R] Matrix\\ m\\ n\\ α$$$

Lean4

/-- This is `Matrix.of` bundled as a linear equivalence. -/
def ofLinearEquiv [Semiring R] [AddCommMonoid α] [Module R α] : (m → n → α) ≃ₗ[R] Matrix m n α
    where
  __ := ofAddEquiv
  map_smul' _ _ := rfl

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