direct sum

plural direct sums

1. mathematicscoproduct in some categories, like abelian groups, topological spaces or modules
2. linear algebraA 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.
3. linear algebraA block diagonal matrix interpreted as having its non-zero blocks (which are square matrices) as summands.