coefficients of a matrix

[ario]

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,
Ario

[matt grime]

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.