Iteratively applies "fau'a" to each resultant operator until all operators resolve.
Let matrix A = ((1, 2), (3, 4)); then A +(fau'ai) A = A +(fau'a*) A = ((1 +(fau'a*) A, 2 +(fau'a*) A), (3 +(fau'a*) A, 4 +(fau'a*) A)) = (( ((1+1, 1+2), (1+3, 1+4)), ((2+1, 2+2),(2+3, 2+4)) ), ( ((3+1, 3+2), (3+3, 3+4)), ((4+1, 4+2), (4+3, 4+4)) )), which has all of the additions resolve (so the iteration terminates) - the result is a 2-by-2 matrix in which each entry is itself a 2-by-2 matrix. If the operators resolve after differing iteration counts, then the process continues only on the unresolved ones with the resolved ones being held constant and saved.