  The instantaneous Bethe-Salpeter equation, derived from the general
Bethe-Salpeter formalism by assuming that the involved interaction kernel is
instantaneous, represents the most promising framework for the description of
hadrons as bound states of quarks from first quantum-field-theoretic
principles, that is, quantum chromodynamics. Here, by extending a previous
analysis confined to the case of bound-state constituents with vanishing
masses, we demonstrate that the instantaneous Bethe-Salpeter equation for
bound-state constituents with (definitely) nonvanishing masses may be converted
into an eigenvalue problem for an explicitly - more precisely, algebraically -
known matrix, at least, for a rather wide class of interactions between these
bound-state constituents. The advantages of the explicit knowledge of this
matrix representation are self-evident.
