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Conditional number of synchronization-time matrix

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I was reading through this 2011 publication in journal Chaos titled "A phase-synchronization and random-matrix based approach to multichannel time-series analysis with application to epilepsy". Here is the link to the paper: www.ncbi.nlm.nih.gov/pmc/articles/PMC3172996/ I would like to make some observations on the section of "choice of diagonal elements" in this paper: