# Find a basis for the space of symmetric nxn matrices

• August 28th 2011, 06:09 AM
hmmmm
Find a basis for the space of symmetric nxn matrices
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.
• August 28th 2011, 06:45 AM
alexmahone
Re: Find a basis for the space of symmetric nxn matrices
Quote:

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?