16.-Linear-Algebra-by-Kenneth-Hoffman · Problem 7.2.20
The Rational and Jordan Forms
Mathematics — Linear Algebra · cyclic-vectors-irreducible-characteristic-polynomial
Problem
Let V be a finite-dimensional vector space over the field F, and let T be a linear operator on V. We ask when it is true that every non-zero vector in V is a cyclic vector for T. Prove that this is the case if and only if the characteristic polynomial for T is irreducible over F.