Parodi's Theorem

The Eigenvalues $\lambda$ satisfying $P(\lambda)=0$, where $P(\lambda)$ is the Characteristic Polynomial, lie in the unions of the Disks

$$\vert z\vert\leq 1$$

$$\vert z+b_1\vert\leq\sum_{j=1}^n \vert b_j\vert.$$

References

Gradshteyn, I. S. and Ryzhik, I. M. Tables of Integrals, Series, and Products, 5th ed. San Diego, CA: Academic Press, p. 1119, 1979.