Re: How to construct symmetric matrix from just a one

• To: mathgroup at smc.vnet.net
• Subject: [mg110375] Re: How to construct symmetric matrix from just a one
• From: Daniel Lichtblau <danl at wolfram.com>
• Date: Wed, 16 Jun 2010 05:36:23 -0400 (EDT)

```dragec wrote:
> symmetric matrix from given just a half matrix with diagonal.
> Eg:
>
> From:
> 1  0  0  0
> 2  3  0  0
> 4  9  5  0
> 2  2  3  4
>
> To give:
>
> 1  2  4  2
> 2  3  9  2
> 4  9  5  3
> 2  2  3  4

Any of these should do the job.

symmetrize1[mat_] := mat + Transpose[mat] -
DiagonalMatrix[Diagonal[mat]]

symmetrize2[mat_] := With[{n=Length[mat]},
Table[If[i<j,mat[[j,i]],mat[[i,j]]], {i,n}, {j,n}]]

symmetrize3[mat_] := With[{n=Length[mat]},
Table[Join[mat[[i,1;;i]],mat[[i+1;;n,i]]], {i,n}]]

Daniel Lichtblau
Wolfram Research

```

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