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Re: matrix manipulation

• To: mathgroup at smc.vnet.net
• Subject: [mg132415] Re: matrix manipulation
• From: Murray Eisenberg <murray at math.umass.edu>
• Date: Mon, 10 Mar 2014 04:41:33 -0400 (EDT)
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• References: <20140308074331.2B3106A1D@smc.vnet.net>

Here's one way (assuming Mathematica 9). I omit the "[i]" part so as not 
to further obscure my code; you may readily insert it. And I chance 
upper-case C to lower-case c (it's best to avoid at least those 
upper-case letters that have built-in meaning).

      topIndices =
          Select[Flatten[Outer[List, Range[6], Range[6]], 1],
          First@# <= Last@# &];

     pattern = {k_, j_} -> Rule[{k, j}, Subscript[c, k, j]];

     mat = Normal@
           SymmetrizedArray[topIndices /. pattern, {6, 6}, Symmetric[{2, 1}]]

     SymmetricMatrixQ[mat]
   (* True *)

On Mar 8, 2014, at 2:43 AM, dimanag78 at gmail.com wrote:

> Hello to all.
>
> I have the following 6x6 matrix
>
> Table[Subscript[C, k, j][i], {k, 1, 6}, {j, 1, 6}]
>
> I want this matrix to be symmetric, that is,
> Subscript[C, k, j][i] = Subscript[C, j, k][i] for j != k.
>
> In other words I want the matrix
>
> {{Subscript[C, 1, 1][i], Subscript[C, 1, 2][i], Subscript[C, 1, 3][i],
>   Subscript[C, 1, 4][i], Subscript[C, 1, 5][i],
>  Subscript[C, 1, 6][i]}, {Subscript[C, 1, 2][i],
>  Subscript[C, 2, 2][i], Subscript[C, 2, 3][i], Subscript[C, 2, 4][i],
>   Subscript[C, 2, 5][i],
>  Subscript[C, 2, 6][i]}, {Subscript[C, 1, 3][i],
>  Subscript[C, 2, 3][i], Subscript[C, 3, 3][i], Subscript[C, 3, 4][i],
>   Subscript[C, 3, 5][i],
>  Subscript[C, 3, 6][i]}, {Subscript[C, 1, 4][i],
>  Subscript[C, 2, 4][i], Subscript[C, 3, 4][i], Subscript[C, 4, 4][i],
>   Subscript[C, 4, 5][i],
>  Subscript[C, 4, 6][i]}, {Subscript[C, 1, 5][i],
>  Subscript[C, 2, 5][i], Subscript[C, 3, 5][i], Subscript[C, 4, 5][i],
>   Subscript[C, 5, 5][i],
>  Subscript[C, 5, 6][i]}, {Subscript[C, 1, 6][i],
>  Subscript[C, 2, 6][i], Subscript[C, 3, 6][i], Subscript[C, 4, 6][i],
>   Subscript[C, 5, 6][i], Subscript[C, 6, 6][i]}}
>
>
> Thank you very much, in advance, for yor help.
>

=97=97
Murray Eisenberg                                murray at math.umass.edu
Mathematics & Statistics Dept.      
Lederle Graduate Research Tower      phone 240 246-7240 (H)
University of Massachusetts               
710 North Pleasant Street                
Amherst, MA 01003-9305

• References:
  • matrix manipulation
    • From: dimanag78@gmail.com