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Let $V_n=(v_{ij})_{i \\leq n,\\, j\\leq m}$ be a $n\\times m$ random matrix, where $(n/m)\\to y > 0$ as $ n \\to \\infty$, and let $X_n=(1/m) V_n V^{*}_n $ be the sample covariance matrix associated to $V_n \\:$. Consider the spectral decomposition of $X_n$ given by $ U_n D_n U_n^{*}$, where $U_n=(u_{ij})_{n\\times n}$ is an eigenmatrix of $X_n$. 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