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A random matrix is a matrix whose entries consist of random variables from some specified distribution. Random matrices have many modern applications in physics, finance, statistics and numerical analysis.

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Eigenvectors of a Wishart matrix

Assume $\Sigma = I_p$. The eigenvectors of $X^TX$ are the right singular vectors of $X$, e.g., $v_1,...,v_r$ with $r=\min(n,p)$ if the SVD of $X$ is $X=\sum_{i=1}^r s_i u_i v_i^\top$. You wish to prov …
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