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May any colleague help us with the following problem.

We have encountered an infinite matrix (occupied by positive integers and zeros). The column space of the matrix could be in parts interpreted as sequences but not sure if there is an overall order.

We do not know much about random matrices, except of the basics. Does there exist a standard simple method, a kind of protocol, how to determine whether a matrix as such is a random matrix or not? and if it would be a random matrix how to identify what type?

Thanks in advance

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Can you compute its spectrum? – Start wearing purple May 2 '13 at 7:34
yes I can calculate the eigenvalues that are two - rest zero. The matrix is lower triangular (all above diagonal zeros). – al-Hwarizmi May 5 '13 at 17:44
then the matrix can not be of one of the standard types used in random matrix theory. – Start wearing purple May 11 '13 at 14:48

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