Linear Algebra Done Right · Problem 5C.11

Eigenvalues, Eigenvectors, and Invariant Subspaces — Sheldon Axler

Mathematics — Linear Algebra · upper-triangular-matrices

Problem

Suppose

\mathbf{F} = \mathbf{C}

and

V

is finite-dimensional. Prove that if

T \in \mathcal{L}(V)

, then there exists a basis of

V

with respect to which

T

has a lower-triangular matrix.