  In this paper, we study the matrix denosing model $Y=S+X$, where $S$ is a
low-rank deterministic signal matrix and $X$ is a random noise matrix, and both
are $M\times n$. In the scenario that $M$ and $n$ are comparably large and the
signals are supercritical, we study the fluctuation of the outlier singular
vectors of $Y$. More specifically, we derive the limiting distribution of
angles between the principal singular vectors of $Y$ and their deterministic
counterparts, the singular vectors of $S$. Further, we also derive the
distribution of the distance between the subspace spanned by the principal
singular vectors of $Y$ and that spanned by the singular vectors of $S$. It
turns out that the limiting distributions depend on the structure of the
singular vectors of $S$ and the distribution of $X$, and thus they are
non-universal.
