Spectra of principal submatrices of nonnegative matrices

✍ Scribed by Thomas J. Laffey; Helena Šmigoc

• Publisher: Elsevier Science
• Year: 2008
• Tongue: English
• Weight: 139 KB
• Volume: 428
• Category: Article
• ISSN: 0024-3795
• DOI: 10.1016/j.laa.2007.06.029

✦ Synopsis

Let A be an n × n nonnegative matrix with the spectrum (λ 1 , λ 2 , . . . , λ n ) and let A 1 be an m × m principal submatrix of A with the spectrum (μ 1 , μ 2 , . . . , μ m ). In this paper we present some cases where the realizability of (μ 1 , μ 2 , . . . , μ m , ν 1 , ν 2 , . . . , ν s ) implies the realizability of (λ 1 , λ 2 , . . . , λ n , ν 1 , ν 2 , . . . , ν s ) and consider the question of whether this holds in general. In particular, we show that the list (λ 1 , λ 2 , . . . , λ n , -μ 1 , -μ 2 , . . . , -μ m ) is realizable.