Square matrix where the coefficients of the diagonal are 1

[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.

 

[M98Ranger]

Hi Ario,

Thank you for sharing your problem with us. It seems like you are trying to solve for the roots of a function that is constant and equal to 1. In this case, there are no solutions since the function is always equal to 1, regardless of the value of w.

One way to avoid this problem is to take a closer look at the matrix and its coefficients. Is there a specific pattern or structure to the coefficients that can help you determine the roots? Can you use any other methods or techniques to solve for the roots instead of relying on the determinant? Additionally, if the matrix is large, you can try using a computer program or calculator to help you find the roots more efficiently.

I hope this helps and good luck with your problem-solving!