Complex sentence: Since "f" "k" is alternating it induces a unique linear map Λ "k" ("V ") →"C " ℓ ("V ","Q").
Split into simpler sentences: Since "f" "k" is alternating it induces a unique linear map. The direct sum of these maps gives a linear map between Λ ("V ") and"C " ℓ ("V ","Q").