Singular vector and singular subspace distribution for the matrix denoising model

In this paper, we study the matrix denoising model $Y=S+X$, where $S$ is a low rank deterministic signal and $X$ random noise matrix, both are $M\times n$. scenario that $M$ $n$ comparably large signals supercritical, fluctuation of outlier singular vectors $Y$, under fully general assumptions on structure distribution $X$. More specifically, derive limiting angles between principal $Y$ their counterparts, $S$. Further, also distance subspace spanned by It turns out distributions depend $X$, thus they nonuniversal. Statistical applications our results to vector inferences discussed.