http://openproblemgarden.org/op/a_nowhere_zero_point_in_a_linear_mapping Comments for "A nowhere-zero point in a linear mapping" en http://openproblemgarden.org/op/a_nowhere_zero_point_in_a_linear_mapping <table cellspacing="10"> <tr> <td> Author(s): <a href="/category/jaeger">Jaeger</a>&nbsp;&nbsp; </td> <td align=right> Subject: <a href="/category/combinatorics">Combinatorics</a> » <a href="/category/matrices">Matrices</a>&nbsp;&nbsp; </td> </tr> <tr> <td colspan=2> <table border=1 cellspacing="5"> <tr><td> <div class="envtheorem"><b>Conjecture</b>&nbsp;&nbsp; If <img class="teximage" src="/files/tex/0996310fb2d1a49c39f098ca07ee5323bf728b79.png" alt="$ {\mathbb F} $" /> is a finite field with at least 4 elements and <img class="teximage" src="/files/tex/7a8d9782350e8eb5a84c149576d83160492cbdd3.png" alt="$ A $" /> is an invertible <img class="teximage" src="/files/tex/fd981d449b91b1f4889d87406e6aa7d8acfb5d68.png" alt="$ n \times n $" /> matrix with entries in <img class="teximage" src="/files/tex/0996310fb2d1a49c39f098ca07ee5323bf728b79.png" alt="$ {\mathbb F} $" />, then there are column vectors <img class="teximage" src="/files/tex/817584f802a24b69508ae913bf47b34d6ff78ca8.png" alt="$ x,y \in {\mathbb F}^n $" /> which have no coordinates equal to zero such that <img class="teximage" src="/files/tex/6fc49872cdb030ca09b427d20b9fd3b1d3873641.png" alt="$ Ax=y $" />. </div> </tr></td> </table> </td> </tr> </table> Jaeger, Francois invertible nowhere-zero flow Combinatorics Matrices http://openproblemgarden.org/op/a_nowhere_zero_point_in_a_linear_mapping#comment Thu, 08 Mar 2007 13:38:56 +0100 mdevos 148 at http://openproblemgarden.org