The matrix direct sum of n matrices constructs a block diagonal matrix from a set of square matrices, i.e., ⊕_(i = 1)^n A_i | = | diag(A_1, A_2, ..., A_n) | = | [A_1 | | | | A_2 | | | | ⋱ | | | | A_n].

block diagonal matrix | Kronecker sum