Find a basis for the space of symmetric nxn matrices

**hmmmm** · Aug 28th 2011, 06:09 AM

Question is in the title really, but I don't really understand what I am required to do, any help understanding the question would be appreciated.

Thanks for any help.

**alexmahone** · Aug 28th 2011, 06:45 AM

Originally Posted by hmmmm

Question is in the title really, but I don't really understand what I am required to do, any help understanding the question would be appreciated.

Thanks for any help.

For n = 3, a basis would be:

$\left[ \begin{array}{ccc} 1 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{array} \right], \left[ \begin{array}{ccc} 0 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 0 \end{array} \right], \left[ \begin{array}{ccc} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 1 \end{array} \right], \left[ \begin{array}{ccc} 0 & 1 & 0 \\ 1 & 0 & 0 \\ 0 & 0 & 0 \end{array} \right], \left[ \begin{array}{ccc} 0 & 0 & 1 \\ 0 & 0 & 0 \\ 1 & 0 & 0 \end{array} \right], \left[ \begin{array}{ccc} 0 & 0 & 0 \\ 0 & 0 & 1 \\ 0 & 1 & 0 \end{array} \right]$

Do you get the idea?

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