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What matrix is this?

  1. Jan 18, 2014 #1
    1. The problem statement, all variables and given/known data

    The matrix
    1 2 -3
    2 5 -4
    -3 -4 6
    is a symmetric matrix by my reckoning. Although in this MCQ that is not an option. The options are
    a)Hermitian
    b)antisymmetric
    c)orthogonal
    d)idempotent

    3. The attempt at a solution

    Hermitian should have complex entities, we have none, so it is not Hermitian
    antisymmetric should be -A=AT and this does not obey that rule, so ruled out.
    orthogonal should have AT=A-1 again not in this case
    idempotent should be A*A=A, again this does not obey

    So what should be the answer?
     
  2. jcsd
  3. Jan 18, 2014 #2

    Ray Vickson

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    Science Advisor
    Homework Helper

    Who says the entries of the matrix are not complex? A real number is a complex number with imaginary part = 0.
     
  4. Jan 18, 2014 #3
    Of course, stupid me. Then it is Hermitian since if I consider all img parts to be 0 then the matrix which I previously assumed to symmetric will just become a Hermitian since the conjugate of a matrix with img part=0 is itself. Thanks Ray.
     
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