Re: Finding determinants of nxn matrices

*To*: mathgroup at smc.vnet.net*Subject*: [mg31805] Re: [mg31758] Finding determinants of nxn matrices*From*: Andrzej Kozlowski <andrzej at tuins.ac.jp>*Date*: Sun, 2 Dec 2001 04:25:57 -0500 (EST)*Sender*: owner-wri-mathgroup at wolfram.com

Here is the complete solution for the case n=3. I hope it is self-explanatory. In[1]:= lambda[A_?MatrixQ]:=Abs[Det[Minors[A]]] In[2]:= matrices=Union[ Map[Partition[#,3]&, Map[ReplacePart[#,6,3]&,Distribute[Table[Range [-1,1],{3^2}],List]]]]; In[3]:= Length[matrices] Out[3]= 6561 In[4]:= largest=Max[lambda/@matrices] Out[4]= 196 In[5]:= Count[matrices,_?(lambda[#]==largest&)] Out[5]= 128 On Saturday, December 1, 2001, at 04:44 PM, cavc_uk wrote: > > 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 > > > Andrzej Kozlowski Toyama International University JAPAN http://platon.c.u-tokyo.ac.jp/andrzej/