ELA, Volume 15, pp. 215-224, August 2006, abstract.

Regions Containing Eigenvalues of a Matrix

Ting-Zhu Huang, Wei Zhang, and Shu-Qian Shen

In this paper, regions containing eigenvalues of a matrix are
obtained in terms of partial absolute deleted row sums and column
sums. Furthermore, some sufficient and necessary conditions for
H-matrices are derived. Finally, an upper bound for the Perron root
of nonnegative matrices is presented. The comparison of the new
upper bound with the known ones is supplemented with some examples.