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Coefficients of a matrix

  1. Jun 24, 2004 #1
    Hallo everybody.
    I have a square matrix where the coefficients of the diagonal are 1, while the others are very small (say 10^-6). Of course the determinant of this matrix will be always one.
    This is my problem:
    the coefficients are functions of a variable (w, complex variable). So, the determinant of the matrix will be a function of w. I need to find the solutions, the roots w of this function (the determinant=0), but since the diagonal is made of 1 and the other coeffs are very small, this function will be constant and equal to 1.
    How can I avoid this problem...extracting the diagonal...
    I tried to normalize the other small coefficients using new variables but they still are very small.
    Thank you for your help,
  2. jcsd
  3. Jun 24, 2004 #2

    matt grime

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    Being small in abs value and being zero aren't the same thing. also what is the size of the matrix? if it is a 10**6 by 10**6 matrix then the small entries may contribute significantly to the determinant. other than this it appears you're just using numbers that are too small for your computer to handle.
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