entryAddMonoidHom — Mathlib

English

The algebra map from R to Matrix n n α equals the composite with diagonalRingHom from (n→α).

Русский

Алгебраическое отображение R в Matrix n n α равно композицийному отображению через diagonalRingHom из (n→α).

LaTeX

$$algebraMap R (Matrix n n α) = (diagonalRingHom n α).comp (algebraMap R (n → α))$$

Lean4

/-- Extracting entries from a matrix as an additive monoid homomorphism. Note this cannot be upgraded to
a ring homomorphism, as it does not respect multiplication.
-/
@[simps]
def entryAddMonoidHom (i : m) (j : n) : Matrix m n α →+ α
    where
  toFun M := M i j
  map_add' _ _ := rfl
  map_zero' := rfl

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