16.-Linear-Algebra-by-Kenneth-Hoffman · Problem 7.2.5
The Rational and Jordan Forms
Mathematics — Linear Algebra · t-invariant-subspaces-direct-sum
Problem
Let T be a linear operator on the vector space V over the field F. If f is a polynomial over F and α is in V, let fα=f(T)α. If V1,…,Vk are T-invariant subspaces and V=V1⊕⋯⊕Vk, show that
fV=fV1⊕⋯⊕fVk.