  We establish central limit theorems for principal eigenvalues and
eigenvectors under a large factor model setting, and develop two-sample tests
of both principal eigenvalues and principal eigenvectors. One important
application is to detect structural breaks in large factor models. Compared
with existing methods for detecting structural breaks, our tests provide unique
insights into the source of structural breaks because they can distinguish
between individual principal eigenvalues and/or eigenvectors. We demonstrate
the application by comparing the principal eigenvalues and principal
eigenvectors of S\&P500 Index constituents' daily returns over different years.
