What's the effect of using modular counting in matrices?

[Coolphreak]

let's say for example, I am interested in using mod 2 integers ({0,1}) to get rid of certain coefficients. Now, I am most interested in eigenvalues. How will this affect my eigenvalues compared to the original matrix (normal counting)? Is there anyway I can "retrieve" the original eigenvalues?

 

[matt grime]

Short answer, no.

Your question is equivalent to asking can I recover the roots of P(x) from P(x) mod 2 where P is a polynomial (the characteristic one in this case).

You can't do that.

 

[mathwonk]

or can you recover an integer just from knowing whether it is even or not?