Non-negative Matrix Spectral Radius Of The Sector Is Estimated

This paper investigates the estimating the bounds for the spectral radius of nonnegative matrices, and some good conclusions are obtained. The main contents are as follows:1. The background of this paper and some relevant research performance are summarized, and the research contents in this paper are presented.2. Firstly, the theory of Frobenius is improved. Secondly, based on the property of the characteristic root and the corresponding characteristic vector, new bounds of the spectral radius are obtained, which convergence is studied.3. The upper bounds for the spectral radius of nonnegative matrices are studied. By utilizing two very well known inequalities, a sequence of progressively better upper bounds for the spectral radius of nonnegative matrices is presented. Each element in the sequence is a function of the spectral radius of the arithmetic symmetrization of a power of matrix.4. The symmetric nonnegative matrices which is a special nonnegative matrices is considered. Applying the property that real symmetric matrices can be diagonalizable, a new theorem of estimating the lower bound is given.