Finding determinants of nxn matrices

*To*: mathgroup at smc.vnet.net*Subject*: [mg31758] Finding determinants of nxn matrices*From*: "cavc_uk" <cavc_uk at ntlworld.com>*Date*: Sat, 1 Dec 2001 02:44:24 -0500 (EST)*Sender*: owner-wri-mathgroup at wolfram.com

Hello. I am interested in a number lamda(A) associated with an nxn matrix, A, which mathematica will compute when given the input Abs[Det[Minors[A]]]. I am interested in matrices with all the entries either -1,0 or 1 except that the (1,3) entry must be 6. I want to know how large lamda(A) can possibly be when A is allowed to range over all possible such nxn matrices. NB only for n<=3. I need to write a function in Mathematica which will find that answer and also will tell us for how many of the 3^((n^2)-1) possible matrices that number is actually obtained. Can anyone suggest the best way to go about this problem? Thanks Judith