Timeline for Playing an (invertible) matrix game with two players
Current License: CC BY-SA 2.5
8 events
| when toggle format | what | by | license | comment | |
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| Nov 12, 2010 at 20:44 | comment | added | Gabriel Benamy | No problem. It's a very interesting problem, and after my Linear Algebra class today, I spoke with my professor about it for a few minutes, but he had another class to teach. His thinking is that it should be simple for player A to prevent submatrix <i>B</i> from forming, but didn't really give a constructive strategy. I will certainly try and work on this problem some more over the next few days and come up with something. I personally believe that player B always has a winning strategy when n > 1. | |
| Nov 12, 2010 at 16:40 | comment | added | Anonymous | Thank you for these usefull insights. I was wrong for $n=3$. | |
| Nov 11, 2010 at 23:16 | comment | added | Gerry Myerson | Those who do not wish to pay for the Hartfiel-Loewy paper may see Brualdi, Huang, and Zhan, Singular, nonsingular, and bounded rank completions of ACI-matrices, freely available at math.ecnu.edu.cn/~zhan/papers/BHZ_Final.pdf wherein the Hartfiel-Loewy result comes as Corollary 8 on page 11. No application to our matrix game is given. | |
| Nov 11, 2010 at 22:59 | comment | added | Gabriel Benamy | Thanks; I didn't catch that mistake in my read-through. The article's abstract mentions that it's n + p, so I mistyped it. | |
| Nov 11, 2010 at 22:58 | history | edited | Gabriel Benamy | CC BY-SA 2.5 |
Fixed a typo, r + s = n + p, not n - p.
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| Nov 11, 2010 at 22:39 | comment | added | Gerry Myerson | I'm looking at the review of the Hartfiel-Loewy paper, MR 86a:15009, written by B N Moyls. The meaty part is that if $\det A=0$ then there's an $r$-by-$s$ submatrix with $r+s=n+p$ of rank at most $p-1$. The review says the converse is also true. But there's also some hoopla about independent indeterminates each appearing exactly once, truly marvelous but too long to fit into this comment box. | |
| Nov 11, 2010 at 22:30 | comment | added | Gerry Myerson | Is $r+s=n-p$ right? All your examples have $r+s\gt n$. | |
| Nov 11, 2010 at 21:31 | history | answered | Gabriel Benamy | CC BY-SA 2.5 |