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.