1. The problem statement, all variables and given/known data The question arises from this quote from wikipedia's article about kronecker product: Kronecker sums appear naturally in physics when considering ensembles of non-interacting systems. Let Hi be the Hamiltonian of the i-th such system. Then the total Hamiltonian of the ensemble is I have to write this Htot as a ordinary sum over kronecker products of unity matrix and Hi-s. 2. Relevant equations Kronecker sum for two matrices is defined as If A is n × n, B is m × m and Ik denotes the k × k identity matrix. 3. The attempt at a solution Well, as I undesratnd, now instead of A and B we have simply Hi and there should be sum kind of sum over i. But the Kronecker sum is defined only for a pair of matrices and it isn't commutative, so the order is important. I tried something like this, for three H-s: But it doesn't look very elegant and I have no idea if this could be true. Any advice?