Estimation Of The Numerical Characteristics Of Matrices And Spectral Radius Of Nonnegative Matrices

As an important method and tool in studying mathematics, matrix computations and matrix analysis theory have been widely used in computational mathematics, factor analysis, image processing, control theory, engineering science, fluid mechanics and other fields. The purpose of this thesis is mainly to study the estimation of numerical characteristics of matrices, such as the boundary value estimates of the matrix determinant and the rank, by using the latest upper bound value for the sum of squares of the module of its eigenvalues, and also do some researches on the estimation of the spectral radius of non-negative matrices. The main results and innovations are as follows:①By using the latest upper bound value for the sum of squares of the module of its eigenvalues, some sharpened estimation for the bounds of rank and determinant of matrices are obtained: and the estimations are more accurate than Ky Fan-Hoffman inequality.②Based on some references of the spread of matrix and the spectral radius of natrix, an upper bound for the spectral radius of singular matrix is presented:③Based on some scholars’research theories about upper and lower bounds for the greatest characteristic root of non-negative matrices, we proposed and improved a more accurate value estimation of the spectral radius of non-negative matrices, and some numerical examples are given to show the effectiveness of our results.