Direct sums are defined for a number of different sorts of mathematical objects, including subspaces, matrices, modules, and groups. The matrix direct sum is defined by ⊕_(i = 1)^n A_i | = | diag(A_1, A_2, ..., A_n) | = | [A_1 | | | | A_2 | | | | ⋱ | | | | A_n] (Ayres 1962, pp. 13-14).

Abelian group | direct product | direct summand | group direct product | group direct sum | matrix direct sum | module | module direct sum