direct sum

coproduct in some categories, like abelian groups, topological spaces or modules

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.

A block diagonal matrix interpreted as having its non-zero blocks (which are square matrices) as summands.