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MathGroup Archive 2007

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Re: all the possible minors of a matrix

  • To: mathgroup at smc.vnet.net
  • Subject: [mg73790] Re: all the possible minors of a matrix
  • From: Peter Pein <petsie at dordos.net>
  • Date: Wed, 28 Feb 2007 04:39:19 -0500 (EST)
  • References: <es13bi$o3s$1@smc.vnet.net>

Mark Novak schrieb:
> Hello,
...
> Minor[m_List?MatrixQ, {i_Integer, 
> j_Integer}]:=Abs[Drop[Transpose[A],{j}]],{i}]]
> Permanent[m_List]:=With[{v=Array[x,Length[m]]},Coefficient[Times@@(m.v),Times@@v]]
> 
> Then the following does work....
> 
> Minor[Abs[A],{1,3}]//MatrixForm
> Permanent[Minor[Abs[A],{i,j}]]/.{i->1,j->1}
> 
> But the problem is that while I can do each of the Minor and Permanent 
> calculations for specified rows i & columns j of the matrix, I can't 
> figure out how to do all n x n possible combinations of i and j.
> 
> Any suggestions would be much appreciated.
> Thanks!
> -mark
> 

Hi Mark,

use Outer:

B = Outer[Permanent[Minor[Abs[A], {##}]] &,
    Sequence @@ Range /@ Dimensions[A], 1]


hth,
Peter


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