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Localization of Perron roots. (English) Zbl 1067.15004
The localization of the Perron root of a nonnegative irreducible matrix is discussed. Recall the spectral radius of a complex matrix \(A\) is defined as the maximum of absolute values of its eigenvalues. It is known that if a real matrix is irreducible and nonnegative then its spectral radius is its eigenvalue (the Perron root). A new localization method giving relationship between the Perron root of a nonnegative matrix and the estimates of the row sums of its generalized Perron complements is given. Some numerical examples are presented.

15A18 Eigenvalues, singular values, and eigenvectors
15B48 Positive matrices and their generalizations; cones of matrices
Full Text: DOI
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