Linear Algebra Done Right · Problem 5C.6

Eigenvalues, Eigenvectors, and Invariant Subspaces — Sheldon Axler

Mathematics — Linear Algebra · upper-triangular-matrices

Problem

Suppose

\mathbf{F} = \mathbf{C}

V

is finite-dimensional, and

T \in \mathcal{L}(V)

. Prove that if

k \in \{1, \ldots, \dim V\}

, then

V

has a

k

-dimensional subspace invariant under

T