MathDB

Prove that these two statements are equivalent for an

n

dimensional vector space

V

\cdot

For the linear transformation

T:V\longrightarrow V

there exists a base for

V

such that the representation of

T

in that base is an upper triangular matrix.

\cdot

There exist subspaces

\{0\}\subsetneq V_1 \subsetneq ...\subsetneq V_{n-1}\subsetneq V

such that for all

i

T(V_i)\subseteq V_i

Problem Statement