I have one question regarding how to measure the correlation between minimum singular values of submatrices extracted from a large random matrix.

Given a m*n random matrix $\mathbf{A}$, the submatrices of it are generated by randomly selecting n out of m rows. Let $\sigma_{\mathrm{min},i}$ be the minimum singular value of submatrix $i$. Obviously, there is correlation between these minimum singular values. The question is how can we measure such correlation in simulation or analytic manner? Is there any difference if the matrix $\mathbf{A}$ is a real matrix or complex matrix?

Thanks a lot!!


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