Kunze Linear Algebra · Problem 7.2.17

Rational and Jordan Forms

Mathematics — Methods · t-invariant-complementary-subspace

Problem

Let TT be a linear operator on a finite-dimensional vector space VV. Suppose that (a) the minimal polynomial for TT is a power of an irreducible polynomial; (b) the minimal polynomial is equal to the characteristic polynomial. Show that no non-trivial TT-invariant subspace has a complementary TT-invariant subspace.

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