16.-Linear-Algebra-by-Kenneth-Hoffman · Problem 7.2.2
The Rational and Jordan Forms
Mathematics — Linear Algebra · t-invariant-complementary-subspaces
Problem
Let T be a linear operator on the finite-dimensional space V, and let R be the range of T.
(a) Prove that R has a complementary T-invariant subspace if and only if R is independent of the null space N of T.
(b) If R and N are independent, prove that N is the unique T-invariant subspace complementary to R.