Re: matrix manipulation

• To: mathgroup at smc.vnet.net
• Subject: [mg132399] Re: matrix manipulation
• From: Roland Franzius <roland.franzius at uos.de>
• Date: Mon, 10 Mar 2014 04:36:13 -0400 (EDT)
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• References: <lfeio3\$5r1\$1@smc.vnet.net>

```Am 08.03.2014 09:01, schrieb dimanag78 at gmail.com:
> 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.
>

Avoid C, its reserved.

Use more advanced procedures like Outer and  Array with Sort.

Outer[Sort[{#1,#2}]&, #, #]&[Range[6]]
gives you the Matrix of a list of sorted pairs of indices from Range
which is of course symmetric.

(Outer[ ( Subscript[k, Sequence @@ Sort[{#1, #2}]] &), #, #] &)[
Range[6]]

You can use this method directly in array contructions

A = Array[Subscript[k, Sequence @@ Sort[{#1, #2}]] &, {6, 6}]

If you have already an array A of expressions, you can symmetrize it later

B=1/2 (A+Transpose[A])

For compactness and shielding from simplifikations I prefer number
strings as indizes

Array[Superscript[k,
StringJoin @@ ToString /@ Sort[{#1, #2}]] &, {6, 6}]

--

Roland Franzius

```

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