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Suppose one is trying to devise a method to generate random matrices with a certain distribution. How does one verify that the generated matrices follow the desired distribution? In particular, I am interested in uniformly distributed random orthogonal matrices, but I am curious how people test their codes for correctness in general.

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In the following article, an experiment is devised to show that the distribution of the largest eigenvalue is given by the Tracy-Widom distribution. See section 10. Perhaps you could modify it.

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    I fail to see what part of Sectio$n$ 10 is related to Victor's question and will be grateful if you provide some e$x$pla$n$ations.2011-03-26