How to go about proving this statement?
Suppose V is finite dimensional and U is a subspace of V . Prove that there exists a subspace W of V such that V = U + W and U ∩ W = {0}, where 0 is the additive identity of V .
Asked
Active
Viewed 266 times
0
-
I have verified with certain examples, which hold true, I am looking for a formal proof to this. – Fenil Feb 18 '17 at 06:52
-
1Start with a basis of $U$, then extend it to a basis of $V$. Let $W$ be the span of the basis elements not in $U$. – angryavian Feb 18 '17 at 07:03
-
Related : see here – Chinnapparaj R Feb 18 '17 at 07:38
1 Answers
0
Take a basis $B$ of $U$, and complete this basis $B\cup B_c$ into a basis of $V$
$W = \text{Span}(B_c)$ is a possible answer
Tryss
- 14,490
- 20
- 35