Let $X$ be a vector space, $V$ and $W$ are subspaces of $X$. Then I would like somebody to help on showing that $X$ is a direct sum of $V$ and $W$ if and only if $x\in X$ has a unique representation $x=v+w$, for some $v\in V$ and $w\in W$. Thanks in advance!
Showing that $X=U\oplus W$
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linear-algebra
vector-spaces
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4What definition of direct sum do you have? That $X = V + W$ et $V \cap W = \{0\}$? What have you tried? – 2012-05-27