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Strange square matrix question

  1. Aug 17, 2013 #1
    1. The problem statement, all variables and given/known data

    Show that for a square matrix the (i,j) entry is equlivant to the (j,i) entry in a symmetric matrix.



    2. Relevant equations



    3. The attempt at a solution

    I just felt this question was weird. They don't give the answers so I'm looking for confirmation.

    I guess you could just do
    ## A = n## x ## n ##
    If symmetric
    ## A = A^T ##
    Consider the defination of A, then, ##( n ## x ## n)^T = n ## x ## n ##
    Implies (i,j) = (j,i)

    I don't know maybe this way?
     
  2. jcsd
  3. Aug 17, 2013 #2

    BruceW

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    what does n x n mean? just the dimensions of the matrix? So, you've shown the transposed matrix has the same dimensions as the original one, but I don't see how this implies (i,j)=(j,i)... Are you familiar with index notation? And how the transpose of a matrix looks in index notation?

    edit: uhhhh... you're right, it is a strange question. It seems to be pretty much asking you to just write down the definition. But I think your teacher/professor would be happier if you said something about index notation of matrices.
     
    Last edited: Aug 17, 2013
  4. Aug 17, 2013 #3

    vela

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    You need to show that ##A=A^T## implies ##a_{ij} = a_{ji}##. Those are two different statements. Start by considering what exactly it means to say that ##A=A^T##.
     
  5. Aug 17, 2013 #4
    Oh yeah I guess that would be better. I just kind of fudged it. I know index notation.
    Thanks dude. It is a dumb question.
     
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