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

  • Thread starter Coolphreak
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  • #1
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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?
 

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  • #2
matt grime
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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.
 
  • #3
mathwonk
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or can you recover an integer just from knowing whether it is even or not?
 

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