       Re: How to construct symmetric matrix from just a one half matrix

• To: mathgroup at smc.vnet.net
• Subject: [mg110373] Re: How to construct symmetric matrix from just a one half matrix
• From: Bill Rowe <readnews at sbcglobal.net>
• Date: Wed, 16 Jun 2010 05:36:00 -0400 (EDT)

```On 6/15/10 at 2:29 AM, culinovic at gmail.com (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

Here is one way that seems reasonably simple:

In:= a = {{1, 0, 0, 0}, {2, 3, 0, 0}, {4, 9, 5, 0}, {2, 2, 3, 4}};
a + Transpose[a] - DiagonalMatrix[Tr[a, List]]

Out= {{1, 2, 4, 2}, {2, 3, 9, 2}, {4, 9, 5, 3},
{2, 2, 3, 4}}

```

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