Let the characteristic polynomial of an complex matrix be written in the form
(1)
| |||
(2)
|
Then for any set of positive numbers with and
(3)
|
all the eigenvalues (for , ..., ) lie on the closed disk in the complex plane.
Let the characteristic polynomial of an complex matrix be written in the form
(1)
| |||
(2)
|
Then for any set of positive numbers with and
(3)
|
all the eigenvalues (for , ..., ) lie on the closed disk in the complex plane.
Weisstein, Eric W. "Ballieu's Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/BallieusTheorem.html