16.-Linear-Algebra-by-Kenneth-Hoffman · Problem 7.2.17
The Rational and Jordan Forms
Mathematics — Linear Algebra · t-invariant-complementary-subspaces
Problem
Let T be a linear operator on a finite-dimensional vector space V. Suppose that
(a) the minimal polynomial for T is a power of an irreducible polynomial;
(b) the minimal polynomial is equal to the characteristic polynomial.
Show that no non-trivial T-invariant subspace has a complementary T-invariant subspace.