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I've done some searching but couldn't get much from the web.

I am looking for some pointers regarding the properties of non-negative non-symmetric square matrices. The elements within the matrix are all real. I know this question is probably a bit general but I'm looking for properties analogous to what we can say for adjacency matrices.

Based on such limited information, what can we say about it's spectrum or bounds? Also, what more can we say if it's trace is zero?

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    $\begingroup$ This question is quite broad. There are whole books written on nonnegative matrices (I'd recommend the one by Berman and Plemmons), so you might have a look to some of them. The Perron-Frobenius theory is one of the fundamental results on this subject. $\endgroup$ – Algebraic Pavel Feb 3 '15 at 10:20
  • $\begingroup$ Thanks Pavel for the pointer. Perron-Frobenius and Gersgorin theorems are the two main results I found so far. $\endgroup$ – Val K Feb 3 '15 at 10:29

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