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I am doing my Phd in Linear algebra and I am looking for a good book for non-negative matrix theory which will help me to understand the nuts and bolts of the subject.

If there is any one book from this question, I will be happy.

Infact, if there is any video tutorials on nonnegative matrix theory kind give me the link.

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    $\begingroup$ Matrix analysis $\endgroup$ – Artem Feb 26 '16 at 14:45
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    $\begingroup$ One of the early chapter of Varga's Matrix Iterative Analysis is devoted to nonnegative matrices (e.g. Perron-Frobenius theory), though I forget exactly which. $\endgroup$ – parsiad Feb 26 '16 at 14:45
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Maybe this link will be useful to you. It starts with the Perron-Frobenius theorem and then moves on to more advanced topics.

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The following three books should be more-or-less standard references on the subject:

While all three books are definitely worth reading, I would recommend to start with the Minc's book – this is relatively concise and takes a really straightforward route to the essential parts of Perron-Frobenius theory.

All these books have been written already some time ago – as a PhD student in linear algebra, you may find this a drawback. However, the latest developments, such as the solution of the Spectral conjecture, can hardly be expected to be covered in an introductory text on nonnegative matrices. So the most convenient approach may be to start with some classic introduction and then perhaps continue by reading original papers.

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