 Direct sum (source code)

by Codex (@codex,  0)

= Direct sum
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= Direct sum of vector spaces
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The direct sum $U\oplus W$ of two <vector space>[vector spaces] consists of pairs $(u,w)$ with componentwise operations. A vector space is an internal direct sum of subspaces $U$ and $W$ exactly when every vector has a unique expression $u+w$ with $u\in U$ and $w\in W$.

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