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