Timeline for Spectrum of primitive nonnegative integer matrices
Current License: CC BY-SA 3.0
9 events
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| Jul 14, 2017 at 22:16 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Jun 14, 2017 at 20:35 | answer | added | Pietro Paparella | timeline score: 2 | |
| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
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| Feb 17, 2015 at 15:44 | comment | added | subshift | Right now the best I can do is to enumerate all the matrices (using the trace constraint) and test them one by one... Can anyone think of a less stupid approach? | |
| Feb 17, 2015 at 15:42 | comment | added | subshift | Gerry, I haven't looked at it for hours but it doesn't seem to be obvious even for $2\times2$ matrices. | |
| Feb 17, 2015 at 15:41 | comment | added | subshift | David, unfortunately I would like to avoid the additional zero eigenvalues. Is this question open even without the primitivity assumption? Thanks for the very interesting articles! | |
| Feb 17, 2015 at 0:10 | comment | added | David Handelman | It would be fascinating to obtain a criterion, let alone an efficient one. Do you permit adding extra zeros as eigenvalues (that is, replacing $p$ by $X^k p$)? Over the reals, it is possible to do this (with criteria in terms of traces of powers, see Boyle & Handelman cited in the reference you cited). Note that $(x-2)(x-1)$ cannot be realized (in your strong sense), but $x(x-2)(x-1)$ can. Reference is another paper by Mike B and me, Algebraic shift equivalence and primitive matrices, tams (1993), which deals mostly with realization over the nonnegative integers. | |
| Feb 16, 2015 at 22:28 | comment | added | Gerry Myerson | Can you do the case $n=2$? | |
| Feb 16, 2015 at 16:25 | history | asked | subshift | CC BY-SA 3.0 |