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How do I set up this matrix

  1. Dec 7, 2016 #1
    1. The problem statement, all variables and given/known data
    A determinant with all elements of order unity may be surprisingly small. The Gilbert determinant Hij=(I+j-1)^-1, i,j=2..... n is notorious for its small values.

    2. Relevant equations


    3. The attempt at a solution
    I just need help setting up the matrix and I can solve it myself. Thanks
     
  2. jcsd
  3. Dec 7, 2016 #2
    I know how to find the numbers for the matrix but I'm confused as to how big the matrix is supposed to be. Am I doing a 1 by 1 then a 2 by 2 then a 3 by3 or am I doing a 3 by 3
     
  4. Dec 7, 2016 #3
    Your notation is a little unclear to me. I assume i represents the matrix row and j represents the matrix column. If that equation is ##H_{ij} = (i+j-1)^{-1}## with dimension equal to 2, then the value of each element is given by this equation with whichever row and column number plugged in.
     
  5. Dec 7, 2016 #4
    Your problem statement doesn't give any direction for actually solving anything. Is there more to it?
     
  6. Dec 7, 2016 #5
    Yes sorry. I'm stuck on the part where it says by order of n=1,2, and 3. What is is asking me to do?. I have already found my matrix using the given equation( it repeats itself in a decreasing way)
     
  7. Dec 7, 2016 #6
    Calculate the value of the Hoover determinant of order n for n=1,2, and 3.

    Is the problem
     
  8. Dec 7, 2016 #7
    If it tells you to solve for an order of 1, 2, and 3, then it's telling you to compute the determinant of a 1x1, 2x2, and 3x3 matrix.
     
  9. Dec 7, 2016 #8
    Quick question. When you are finding the determinant of a matrix. Do the rows and columns have to be equal?
     
  10. Dec 7, 2016 #9
    Yes. You can only take the determinant of a square matrix.
     
  11. Dec 7, 2016 #10
    For my answers I got
    1
    1/12
    And I am working on the third
     
  12. Dec 7, 2016 #11
    For the 3 by 3
    0.00046297
     
  13. Dec 7, 2016 #12
    That looks right!
     
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