i have a question and i got stuck on certain step of the solution.
i'll write the question and the solution till the point where i got stuck
and explain why i got stuck
the question:
there is A 3x3 matrices which have 3 real eigenvalues,
so the jordan form of
find the caracteristic polinomial
and the minimal polinomial of A and write its jordan form.
the solution:
it is given that is similar to .
so the caracteristic polinomial of is
so 8 and 1 are the only eigenvalues.
suppose and so
if and its eigenvalue of A then is eigen value of
so
so
so the possible caracteristic polinomials are:
suppose that or
then the caracteristic polinomial will be or
and thats cannot happen .(stuck on understanding this point)
my probem with this point:
if i know that 8 is eigenvalue of but why the
why we have the same structure??
another problem is why these possible caracteristic polinomials cannot work?