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),
 |
Furthermore, if 
has exactly 
eigenvalues 
on the circle 
, then the set of all its eigenvalues
is invariant under rotations by 
about the origin.
