The Perron eigenspace of nonnegative almost skew-symmetric matrices and Levinger’s transformation
نویسندگان
چکیده
Let A be a nonnegative square matrix whose symmetric part has rank one. Tournament matrices are of this type up to a positive shift by 1/2I . When the symmetric part of A is irreducible, the Perron value and the left and right Perron vectors of L(A, α) = (1 − α)A+ αAt are studied and compared as functions of α ∈ [0, 1/2]. In particular, upper bounds are obtained for both the Perron value and its derivative as functions of the parameter α via the notion of the q-numerical range. © 2002 Elsevier Science Inc. All rights reserved. AMS classification: 15A18; 15A42; 15A60; 05C20
منابع مشابه
Bounds for Levinger’s function of nonnegative almost skew-symmetric matrices
The analysis of the Perron eigenspace of a nonnegative matrix A whose symmetric part has rank one is continued. Improved bounds for the Perron root of Levinger’s transformation (1 − α)A+ αAt (α ∈ [0, 1]) and its derivative are obtained. The relative geometry of the corresponding left and right Perron vectors is examined. The results are applied to tournament matrices to obtain a comparison resu...
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