Timeline for Growth of powers of non-negative integer matrices
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 25, 2013 at 12:16 | answer | added | Igor Rivin | timeline score: 4 | |
| Jul 25, 2013 at 11:30 | comment | added | Denis | If you take the 2*2 matrix [1 1][0 1], you get $a_n=n+2$. | |
| Jul 25, 2013 at 11:26 | comment | added | Victor | Thanks, Henrik. Yes, it would be interesting to learn what could be the growth rates of that sequence. It would be quite surprising if the growth could be intermediate | |
| Jul 25, 2013 at 11:04 | comment | added | HenrikRüping | Let $l(A)$ denote the largest entry in a matrix $A$. Then we have for two $m\times m$ matrices with nonnegative entries $l(AB)\le m\cdot l(A)\cdot l(B)$ and thus $a_n\le m^2l(A^n)\le m^{2+n}l(A)^n$. If we consider the matrix with all entries equal, we get equality and so this bound is as sharp as possible. But I guess you were looking for examples, where this sequence grows polynomially or subexponentially or so. | |
| Jul 25, 2013 at 9:38 | history | asked | Victor | CC BY-SA 3.0 |