- #1

- 46

- 0

Haven't been able to get this one, thanks for your help.

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- Thread starter imurme8
- Start date

- #1

- 46

- 0

Haven't been able to get this one, thanks for your help.

- #2

jgens

Gold Member

- 1,583

- 50

Notice that [itex]V = \bigoplus_{i=1}^k \langle B_i \rangle[/itex], so [itex]S = S \cap V = \bigoplus_{i=1}^k S \cap \langle B_i \rangle[/itex].

- #3

- 46

- 0

Where have you used that [itex]S\cap \langle B_i\rangle \neq \{0\}[/itex] for all [itex]i[/itex]? I can come up with the following counterexample if we do not assume this hypothesis:

In [itex]\mathbb{R}^2[/itex], the subspace [itex]y=x[/itex] is certainly not the direct sum of its intersections with [itex]\langle e_1 \rangle[/itex] and [itex]\langle e_2 \rangle[/itex] (both zero).

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