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A theorem for locating eigenvalues

✍ Scribed by Pan Xiaoshu; Dai Hua

Publisher: Springer Vienna
Year: 1985
Tongue: English
Weight: 181 KB
Volume: 35
Category: Article
ISSN: 0010-485X
DOI: 10.1007/bf02240150

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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 ~<