Condition for a direct sum

Suppose $U_1,\dots,U_m$ are subspaces of $V$. Then $U_1 + \dots + U_m$ is a direct sum if and only if the only way to write $0$ as a sum $u_1 + \dots + u_m$ where each $u_j \in U_j$ is by taking each $u_j = 0$.