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Some lower bounds for the Perron root of a nonnegative matrix

In this paper, we present some lower bounds for the Perron root of a symmetric nonnegative matrix, which are then applied to give the lower bounds of the Perron root of a general nonnegative matrix. These bounds improve the corresponding ones in [3] and [5]. Numerical examples are supplemented to illustrate the effectiveness of the presented bounds. Mathematics subject classification (2010): 15A18, 15A57, 65F15.