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We apply the method of determinants to study the distribution of the largestsingular values of large $ m \times n $ real rectangular random matrices withindependent Cauchy entries. We show that statistical properties of the(rescaled by a factor of $ \frac{1}{m^2\*n^2}$)largest singular values agree inthe limit with the statistics of the inhomogeneous Poisson random point processwith the intensity $ \frac{1}{\pi} x^{-3/2} $ and, therefore, are differentfrom the Tracy-Widom law. Among other corollaries of our method we show aninteresting connection between the mathematical expectations of thedeterminants of complex rectangular $ m \times n $ standard Wishart ensembleand real rectangular $ 2m \times 2n $ standard Wishart ensemble.Comment: We have shown in the revised version that the statistics of the  largest eigenavlues of a sample covariance random matrix with i.i.d. Cauchy  entries agree in the limit with the statistics of the inhomogeneous Poisson  random point process with the intensity $\frac{1}{\pi} x^{-3/2}.

On the largest singular values of random matrices with independent Cauchy entries