Re: Creating a symmetric matrix

• To: mathgroup at smc.vnet.net
• Subject: [mg46859] Re: Creating a symmetric matrix
• From: astanoff at yahoo.fr (astanoff)
• Date: Fri, 12 Mar 2004 02:02:44 -0500 (EST)
• References: <c2p9ld\$dns\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```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

My solution :
In[1]:=
symmetrize[m_]:=
With[{mi=MapIndexed[Table[0,{#2[[1]]}]~Join~Drop[#1,#2[[1]]]&,m]},
mi+Transpose[mi]+IdentityMatrix[Length[m]]*m
];
In[2]:=m={{1,2,3},{0,5,6},{0,0,9}};
In[3]:=symmetrize[m]
Out[3]={{1,2,3},{2,5,6},{3,6,9}}

hth
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