Eigenvalue location for nonnegative and Z-matrices

✍ Scribed by Shaun M. Fallat; Charles R. Johnson; Ronald L. Smith; P. van den Driessche

• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 518 KB
• Volume: 277
• Category: Article
• ISSN: 0024-3795
• DOI: 10.1016/s0024-3795(97)10081-7

✦ Synopsis

Let L~ denote the class of n x n Z-matrices A = tl -B with B ~> 0 and pk(B) <~ t <-Pk+l (B), where pk(B) denotes the maximum spectral radius of k x k principal submatrices of B. Bounds are determined on the number of eigenvalues with positive real parts for A E L~i, where k satisfies, [n/2j ~< k ~< n -1. For these classes, when k = n -1 and n -2, wedges are identified that contain only the unique negative eigenvalue of A. These results lead to new eigenvalue location regions for nonnegative matrices.