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Confused about drawing matrix diagram

  1. Feb 6, 2012 #1
    1. The problem statement, all variables and given/known data
    Give an example of the matrix:
    3x3 upper triangular symmetric matrix


    2. Relevant equations



    3. The attempt at a solution
    I know what an upper triangular matrix and what a symmetric matrix looks like. But what happens when they put it together? Is the symmetry in the upper right portion of the matrix now? Like this?

    1 5 3
    0 2 5
    0 0 3
     
  2. jcsd
  3. Feb 6, 2012 #2

    Mark44

    Staff: Mentor

    What is the definition of a symmetric matrix?
     
  4. Feb 6, 2012 #3
    Numbers are equal across the diagonal.
     
  5. Feb 6, 2012 #4

    Mark44

    Staff: Mentor

    Which diagonal is that?
     
  6. Feb 6, 2012 #5
    Middle diagonal like this:

    1 2 4
    2 3 7
    4 7 5
     
  7. Feb 6, 2012 #6

    Mark44

    Staff: Mentor

    Yes, and that's often called the main diagonal. So if a 3x3 matrix is symmetric and upper triangular, then a12 has to equal a21, for example. Since it is upper triangular, what must a21 equal?
     
  8. Feb 6, 2012 #7
    So you are implying that the symmetric in this this case wouldn't even matter at all since there is upper triangular in it?

    Answer should be something like this?

    1 2 4
    0 3 7
    0 0 5

    Same answer if the problem asked for an upper triangular example?
     
  9. Feb 6, 2012 #8

    Mark44

    Staff: Mentor

    No, I am not saying that. Your matrix in post #7 is not symmetric, because a12 = 2, while a21 = 0.

    Maybe you have a flawed understanding of what "upper triangular" means. How do you define this term?
     
  10. Feb 6, 2012 #9
    Upper triangular would have zeros everywhere southwest of the main diagonal
     
  11. Feb 6, 2012 #10

    Mark44

    Staff: Mentor

    And if such a matrix is also symmetric, what can you conclude?
     
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