I am reading a book of Helgason.
As you know, solvable Lie algebra $g \subset V= {\bf C}^n$ have a nonzero $v$ such that $v$ is an eigenvector of any element of $g$.
I can follow the proof in the book. But the next corollary is : Under the above assumption, $g$ is a set of upper triangular matrices in some basis.
I have a difficulty to prove this.
How can we prove this ? Thank you in advance.