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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