http://openproblemgarden.org/op/elementary_symmetric_of_a_sum_of_matrices Comments for "Elementary symmetric of a sum of matrices" en http://openproblemgarden.org/op/elementary_symmetric_of_a_sum_of_matrices#comment-6786 <p>that's ok</p> Fri, 27 Aug 2010 09:11:43 +0200 olivier comment 6786 at http://openproblemgarden.org http://openproblemgarden.org/op/elementary_symmetric_of_a_sum_of_matrices <table cellspacing="10"> <tr> <td> Author(s): <a href="/kpz_equation_central_limit_theorem"></a>&nbsp;&nbsp; </td> <td align=right> Subject: <a href="/category/algebra">Algebra</a>&nbsp;&nbsp; </td> </tr> <tr> <td colspan=2> <table border=1 cellspacing="5"> <tr><td> <div class="envtheorem"><b>Problem</b>&nbsp;&nbsp;</p> <p>Given a Matrix <img class="teximage" src="/files/tex/7a8d9782350e8eb5a84c149576d83160492cbdd3.png" alt="$ A $" />, the <img class="teximage" src="/files/tex/c450c3185f7285cfa0b88d3a903c54f7df601201.png" alt="$ k $" />-th <a href="http://en.wikipedia.org/wiki/elementary symmetric function">elementary symmetric function</a> of <img class="teximage" src="/files/tex/7a8d9782350e8eb5a84c149576d83160492cbdd3.png" alt="$ A $" />, namely <img class="teximage" src="/files/tex/95ee6b8e112682d8c6cd79b4279c3b34fbeaf88c.png" alt="$ S_k(A) $" />, is defined as the sum of all <img class="teximage" src="/files/tex/c450c3185f7285cfa0b88d3a903c54f7df601201.png" alt="$ k $" />-by-<img class="teximage" src="/files/tex/c450c3185f7285cfa0b88d3a903c54f7df601201.png" alt="$ k $" /> principal minors. </p> <p>Find a closed expression for the <img class="teximage" src="/files/tex/c450c3185f7285cfa0b88d3a903c54f7df601201.png" alt="$ k $" />-th elementary symmetric function of a sum of N <img class="teximage" src="/files/tex/ec63d7020a64c039d5f6703b8fa3ab7393358b5b.png" alt="$ n $" />-by-<img class="teximage" src="/files/tex/ec63d7020a64c039d5f6703b8fa3ab7393358b5b.png" alt="$ n $" /> matrices, with <img class="teximage" src="/files/tex/db4a1f21c4082f991906bfe685d86eebbc147693.png" alt="$ 0\le N\le k\le n $" /> by using partitions. </p> </div> </tr></td> </table> </td> </tr> </table> Algebra http://openproblemgarden.org/op/elementary_symmetric_of_a_sum_of_matrices#comment Mon, 08 Dec 2008 18:44:17 +0100 rscosa 23298 at http://openproblemgarden.org