  In a statistical ensemble with $M$ microstates, we introduce an $M \times M$
correlation matrix with the correlations between microstates as its elements.
Using eigenvectors of the correlation matrix, we can define eigen microstates
of the ensemble. The normalized eigenvalue by $M$ represents the weight factor
in the ensemble of the corresponding eigen microstate. In the limit $M \to
\infty$, weight factors go to zero in the ensemble without localization of
microstate. The finite limit of weight factor when $M \to \infty$ indicates a
condensation of the corresponding eigen microstate. This indicates a phase
transition with new phase characterized by the condensed eigen microstate. We
propose a finite-size scaling relation of weight factors near critical point,
which can be used to identify the phase transition and its universality class
of general complex systems. The condensation of eigen microstate and the
finite-size scaling relation of weight factors have been confirmed by the Monte
Carlo data of one-dimensional and two-dimensional Ising models.
