Perturbation　bounds　for　singular　subspaces　have　a　wide　range　of　applications,　including　high-dimensional　statistics,　machine　learning,　and　applied　mathematics.　This　paper　focuses　on　the　perturbation　bounds　of　singular　subspaces　under　a　signal　matrix　interfered　by　a　special　heteroscedastic　noise　matrix　in　which　its　same　row　or　column　shares　similar　variance.　First　of　all,　we　extend　homoscedastic　results　of　T.　Tony　Cai　and　Anru　Zhang　(see　Rate-optimal　perturbation　bounds　for　singular　subspaces　with　applications　to　high-dimensional　statistics,　The　Annals　of　Statistics,　2018,　46(1),　60-89)　to　heteroscedastic　cases.　Then　we　apply　the　developed　tools　to　the　heteroskedastic　clustering　model.　We　find　out　that　our　upper　bound　of　clustering　misclassification　rate　is　better　than　the　one　of　T.　Tony　Cai,　Rungang　Han,　and　Anru　Zhang　(see　arXiv:2008.12434,　2020).