  Weighted sums of left and right hand Kronecker products of Integer Sequence
Doubly Affine (ISDA) as well as Generalized Arithmetic Progression Doubly
Affine (GAPDA) arrays are used to generate larger ISDA arrays of multiplicative
order (compound squares) from pairs of smaller ones.
  In two dimensions we find general expressions for the eigenvalues (EVs) and
singular values (SVs) of the larger arrays in terms of the EVs and SVs of their
constituent matrices, leading to a simple result for the rank of these highly
singular compound matrices. Since the critical property of the smaller
constituent matrices involves only identical row and column sums (often called
semi-magic), the eigenvalue and singular value results can be applied to both
magic squares and Latin squares. Additionally, the compounding process works in
arbitrary dimensions due to the generality of the Kronecker product, providing
a simple method to generate large order ISDA cubes and hypercubes.
  The first examples of compound magic squares are found in manuscripts that
date back to the 10th century CE, and other representative applications are
outlined through judicious examples.
