If all elements of an Irreducible Matrix
are Nonnegative, then
is an
Eigenvalue of
and all the Eigenvalues of
lie on the Disk

where, if is a set of Nonnegative numbers (which are not all zero),

and . Furthermore, if has exactly Eigenvalues on the Circle , then the set of all its Eigenvalues is invariant under rotations by about the Origin.

**References**

Gradshteyn, I. S. and Ryzhik, I. M. *Tables of Integrals, Series, and Products, 5th ed.* San Diego, CA:
Academic Press, p. 1121, 1979.

© 1996-9

1999-05-26