Definitions from Wiktionary (direct sum)

▸ noun:  (mathematics) coproduct in some categories, like abelian groups, topological spaces or modules
▸ noun:  (linear algebra) A linear sum in which the intersection of the summands has dimension zero. Equivalently, a linear sum of two subspaces, any vector of which can be expressed uniquely as a sum of two vectors: one vector belonging to the first subspace, and the other vector belonging to the second subspace.
▸ noun:  (linear algebra) A block diagonal matrix interpreted as having its non-zero blocks (which are square matrices) as summands.
▸ Also see direct_sum


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