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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.

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