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Can someone provide a formula for $\bigwedge( V_1\oplus V_2\oplus V_3\oplus..)$. The formula for two summands is $\bigwedge^1 (V_1\oplus V_2)=(\wedge^1V_1\otimes \wedge^0V_2) \oplus (\wedge^0V_1\otimes\wedge^1V_2)$ where $V_1,V_2$ are $K$-vector spaces.

Also am I right to assume that $V_1\otimes K=V_1$?

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