Research On The Inverse Characteristic Problems Of Several Types Of Arrow Matrix

The inverse eigenvalue problem of special matrices is an important topic in numerical algebra.In this paper,we study the inverse eigenvalue problems of four special matrices with different structures.In the first chapter,the research background and significance of matrix inverse eigenvalue problem,related basic concepts and current research status are given.In the second chapter,the inverse eigenvalue problems of three kinds of special matrices with different structures are studied.The first two kinds of matrices are symmetric arrowshaped Jacobi matrices which are generalized from path graphs and broom graphs.By using the related properties of arrow matrices and Jacobi matrices,the inverse eigenvalue problem is transformed into the problem of solving linear equations.Finally,the specific conditions for the inverse construction of the first two kinds of matrices are obtained respectively.The third kind of matrix is the form of symmetric arrow matrix plus Jacobi matrix.By using the related properties of arrow matrix,the maximum and minimum eigenvalues of each order principal subformula of the matrix are taken as its characteristic data,and the solvability condition of matrix inverse construction is obtained.In the third chapter,we study the inverse construction of asymmetric matrices in the real number field.Firstly,the inverse construction of tridiagonal claw matrix is studied,and the inverse construction of the matrix is completed by using the maximum and minimum eigenvalues and feature pairs as feature data.Then,based on the research of the third kind of symmetric matrix in the second chapter,the asymmetric form of the matrix is constructed by using a set of characteristic pairs.The validity of the results is verified by numerical simulation of low-order matrices.