  The statistics of random-matrix spectra can be very sensitive to the
unfolding procedure that separates global from local properties. In order to
avoid the introduction of possible artifacts, recently it has been applied to
ergodic ensembles of Random Matrix Theory (RMT) the singular value
decomposition (SVD) method, based on normal mode analysis, which characterizes
the long-range correlations of the spectral fluctuations in a direct way
without performing any unfolding. However, in the case of more general
ensembles, the ergodicity property is often broken leading to ambiguities
between spectrum-unfolded and ensemble-unfolded fluctuation statistics. Here,
we apply SVD to a disordered random-matrix ensemble with tunable nonergodicity,
as a mathematical framework to characterize the nonergodicity. We show that
ensemble-averaged and individual-spectrum averaged statistics are calculated
consistently using the same normal mode basis, and the nonergodicity is
explained as a breakdown of this common basis.
