Localization of Perron roots
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.
scientific article; zbMATH DE number 2119131