0

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.

Leif
  • 1,493
  • 13
  • 26
  • 2
    http://math.stackexchange.com/questions/71872/union-of-two-vector-subspaces-not-a-subspace – mle Feb 07 '17 at 15:40
  • How do you understand this union: in the set-theoretical sense, or in Minkowski sense, i.e. ${u+w:u\in W_1,w\in W_2}$? – szw1710 Feb 07 '17 at 15:41
  • 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. – Thomas Feb 07 '17 at 15:41
  • $\langle W_1 \cup W_2 \rangle =:W_1 +W_2 \neq W_1 \cup W_2$ (http://math.stackexchange.com/questions/839346/the-union-of-two-subspaces-is-a-subset-of-the-sum?rq=1) – mle Feb 07 '17 at 15:43
  • Thank you. And I haven't noticed that similar question was already posted. – Leif Feb 07 '17 at 15:45

0 Answers0