  Matrix diagonalization has long been a setback in the numerical simulation of
the magnetic resonance spectra of multispin systems since the dimension of the
Hilbert space of such systems grows exponentially with the number of spins -- a
problem commonly referred to as the "curse of dimensionality". In this paper,
we propose two mathematical instruments which, when harmoniously combined,
could greatly help surmount to a fair degree and in a systematic manner the
curse of dimensionality. These are: 1) the Holstein-Primakoff bosons and 2)
what we have termed the "index compression maps". These two allow a bijective
mapping of (multi)spin states to integers. Their combination leads to the block
diagonalization of the multispin Hamiltonian, thus a computationally exact way
of diagonalizing the latter but which also reduces significantly the
computational cost. We also show that the eigenvectors and eigenvalues of the
Liouvillian operator can be easily determined once those of the related
multispin Hamiltonian are known. Interestingly, the method also enables an
analytical characterization of the multispin Hilbert space -- a feat hardly
attainable with other approaches.
  We illustrate the method here by showing how a general static isotropic
multispin Hamiltonian could be exactly diagonalized with very less
computational cost. Nonetheless, we emphasize that the method could be applied
to study numerous quantum systems defined on finite Hilbert spaces and embodied
with at most pairwise interactions.
