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Help on showing matrices are symmetric

  1. May 2, 2007 #1
    I'm having trouble understanding a certain matrix problem.

    -Show that AA^T and A^TA are symmetric.
    -Show that A+A^T is symmetric.

    Any help would be greatly appreciated.
    Last edited: May 2, 2007
  2. jcsd
  3. May 2, 2007 #2


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    Showing A+AT is symmetric should be trivial... write out A as an nxn matrix (it needs to be square for addition to be defined!) with entries [tex]a_{i,j}[/tex], and you should be able to calculate directly the i,jth entry of A+AT
  4. May 2, 2007 #3


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    Symmetric means A^T=A. And you know that (A+B)^T=A^T+B^T and (AB)^T=(B^T)(A^T), yes?
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