A certain symmetry is exploited in expressing exact solutions to the focusing
nonlinear Schr\"odinger equation in terms of a triplet of constant matrices.
Consequently, for any number of bound states with any number of multiplicities
the corresponding soliton solutions are explicitly written in a compact form in
terms of a matrix triplet. Conversely, from such a soliton solution the
corresponding transmission coefficients, bound-state poles, bound-state norming
constants and Jost solutions for the associated Zakharov-Shabat system are
evaluated explicitly. It is also shown that these results hold for the matrix
nonlinear Schr\"odinger equation of any matrix size
