Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6416063 | Linear Algebra and its Applications | 2016 | 18 Pages |
Abstract
Let A be an irreducible (entrywise) nonnegative nÃn matrix with eigenvaluesÏ,λ2=b+ic,λ3=bâic,λ4,â¯,λn, where Ï is the Perron eigenvalue. It is shown that for any tâ[0,â) there is a nonnegative matrix with eigenvaluesÏ+tË,λ2+t,λ3+t,λ4,â¯,λn, whenever tË⩾γnt with γ3=1, γ4=2, γ5=5 and γn=2.25 for n⩾6. The result improves that of Guo et al. Our proof depends on an auxiliary result in geometry asserting that the area of an n-sided convex polygon is bounded by γn times the maximum area of a triangle lying inside the polygon.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Xuefeng Wang, Chi-Kwong Li, Yiu-Tung Poon,