Re: Creating a symmetric matrix
- To: mathgroup at smc.vnet.net
- Subject: [mg46878] Re: Creating a symmetric matrix
- From: Roland Franzius <roland.franzius at uos.de>
- Date: Fri, 12 Mar 2004 23:39:24 -0500 (EST)
- Organization: Universitaet Hannover
- References: <200403110850.DAA13986@smc.vnet.net> <c2rnhu$p0s$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
Andrzej Kozlowski wrote:
> On 11 Mar 2004, at 09:50, Mark Coleman wrote:
>
>
>>Greetings,
>>
>>How can I efficiently build a symmetric matrix from an upper triangular
>>one, i.e., extract the upper triangular elements and insert them into
>>the lower triangle in such a way as to make the resulting square matrix
>>symmetric?
>>
>>Thanks,
>>
>>Mark
>>
>>
>>
>
>
> The most natural way must be
>
> A+Tranpose[A]
>
> e.g.
>
> A = Array[KroneckerDelta[#1 < #2, True] & , {3, 3}];
>
>
> {{0, 1, 1}, {0, 0, 1}, {0, 0, 0}}
>
>
> A + Transpose[A]
>
>
> {{0, 1, 1}, {1, 0, 1}, {1, 1, 0}}
Very good compared to the other sugestions!
If the diagonal of A contains elements !=0 the formula is of course for
every Matrix A
Symmetric part:
A_s =1/2 (A+Transpose[A])
antisymmetric trace free part
A_a = 1/2 (a-Transpose[A])
--
Roland Franzius
- References:
- Creating a symmetric matrix
- From: Mark Coleman <mark@markscoleman.com>
- Creating a symmetric matrix