Some applications of the Kronecker product in Hubbard representation

The properties of the Kronecker product are revisited in terms of Hubbard operators. The simplest representation of a Hubbard operator X-n(i,j) is a square matrix of size n with an entry equal to 1 and zero elsewhere. This framework simplifies the calculation of the Kronecker product of arbitrary matrices no matter the size or the number of the involved factors. Some applications are presented, these include the algebra of permutation matrices, the Hadamard matrix, the XXX Heisenberg model and the interaction of an atom with radiation fields.