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Math Help - Find a basis for the space of symmetric nxn matrices

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    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.
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  2. #2
    MHF Contributor alexmahone's Avatar
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    Re: Find a basis for the space of symmetric nxn matrices

    Quote Originally Posted by hmmmm View Post
    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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