Cycle/Minimal polynomial/Exercise
Let the cycle be given, and let denote the corresponding
-permutation matrix
over a field .
a) Let be a polynomial of degree . Establish a formula for .
b) Determine the
minimal polynomial
of .
c) Give an example for an
endomorphism
on a real vector space with different vectors
such that
,
and
holds, and such that the minimal polynomial of is not .