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For which conditions is the union of two subspaces $W_1 \lor W_2$ also a subspace?

So $W_1$ is a subspace and $W_2$ is a subspace, hence we can choose $u \in W_1$ and $v \in W_2$ and for the union we have $u + v$.

So the vector $(u + v)$ must lie in the intersection of these subspaces?

Thanks for helping me.

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    http://math.stackexchange.com/questions/71872/union-of-two-vector-subspaces-not-a-subspace – 2017-02-07
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    How do you understand this union: in the set-theoretical sense, or in Minkowski sense, i.e. $\{u+w:u\in W_1,w\in W_2\}$? – 2017-02-07
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    Just have a look at two lines in Euclidean two space or a line and a two dimensional subspace in Euclidean three space to get an idea. – 2017-02-07
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    $\langle W_1 \cup W_2 \rangle =:W_1 +W_2 \neq W_1 \cup W_2$ (http://math.stackexchange.com/questions/839346/the-union-of-two-subspaces-is-a-subset-of-the-sum?rq=1) – 2017-02-07
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    Thank you. And I haven't noticed that similar question was already posted. – 2017-02-07

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