  In this paper, we propose an approach of the nucleon-pair approximation
(NPA), in which the collective nucleon pairs are represented in terms of
antisymmetric matrices, and commutations between nucleon pairs are given by
using matrix multiplication that avoids angular-momentum couplings and
recouplings. Therefore the present approach significantly simplifies the NPA
computation. Furthermore, it is formulated on the same footing with and without
isospin.
