Let V i , , V n be vector spaces over the same field F Define the direct sum V 1 V n of the vectors spaces V i for i 1, , n, and show that the direct sum is again a vector space over F

Question: Let V i , , V n be vector spaces over the same field F. Define the direct sum V 1

Let V_i, ··· , V_n be vector spaces over the same field F. Define the direct sum V₁ ⊕ ··· ⊕ V_n of the vectors spaces V_i for i = 1, ···, n, and show that the direct sum is again a vector space over F.

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