Definition of direct sum of subspaces

Created almost 9 years ago, updated about 8 hours ago

The sum $U+W$ is direct, written $U\oplus W$, if every vector in the sum has a unique decomposition $u+w$. For two subspaces this is equivalent to $U\cap W=\{0\}$. For several subspaces, pairwise zero intersections alone do not guarantee a direct sum.

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