# Coefficients of a matrix

1. Jun 24, 2004

### 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.