The Inverse Eigenvalue Problem For Arrow-like Matrices

Discussing the particle of the quality or spring’s rigidity is inverse problem of vibrating system by the system’s partial frequencies(characteristic value)and the corresponding mode of vibration(characteristic vector).There are the non-varishing elements in the first row, the first column and the diagonal line of the matrices. The only condition for the existence of solution is proved and gives concrete expression of solution.In the first chapter,we discuss the background of the inverse eigenvalue problems for matrices and introduce the structure of this paper. The specific contents include from the inverse eigenvalue of matrices,the inverse eigenvalue problems for arrow shape matrices. We introduce the background and advances of inverse problem.The second chapter is the most important of this paper. it describes the generalized inverse eigenvalue problem for four kind of arrow matrices in views of sweepback matrices and the linear relationship characteristic value inverse. Disussing the sufficient conditions of problems which have a unique solution, the expression of the solution of the problem is given, some numerical example is provided.The third part is also the main content.it describes the generalized inverse eigenvalue problem of arrow shape matrices of lack of some part. Inverse eigenvalue problem for sub-periodic generalized Jacobi Matrices with linear relation.Discussing the sufficient conditions of the problem which have a unique solution.In the fourth part,we discuss the generalized inverse eigenvalue problem of arrow shape matrices,which is minimum matrix norum.