Guo perturbation for symmetric nonnegative circulant matrices

✍ Scribed by Oscar Rojo; Ricardo L. Soto

• Publisher: Elsevier Science
• Year: 2009
• Tongue: English
• Weight: 200 KB
• Volume: 431
• Category: Article
• ISSN: 0024-3795
• DOI: 10.1016/j.laa.2009.03.009

✦ Synopsis

Guo [W. Guo, Eigenvalues of nonnegative matrices, Linear Algebra Appl. 266 (1997) 261-270] sets the question: if the list Λ = {λ 1 , λ 2 , . . . , λ n } is symmetrically realizable (that is, Λ is the spectrum of a symmetric nonnegative matrix), and t > 0, whether or not the list Λ t = {λ 1 + t, λ 2 ± t, λ 3 , . . . , λ n } is also symmetrically realizable. In this paper we give an affirmative answer to this question in the case that the realizing matrix is circulant or left circulant.

We also give a necessary and sufficient condition for Λ to be the spectrum of a nonnegative left circulant matrix.