According to isolation property an unreduced symmetric tridiagonal matrix with eigenvalues, we give an equivalence model with subsection strict monotonically.

In this paper,the inverse problems of constructing the irreducible tridiagonal matrixes,Jacobi matrixes and negative Jacobi matrixes with given three vector pairs are discussed.

This paper provides two FORTRAN subroutines for the two computational problems of the symmetric tridiagonal matrix (solution of the system of liner algebraic equations, and computation of the generalized eigenvalues and eigenvectors).

First, an unsymmetric tridiagonal matrix T is transformed into a symmetric tridiagonal matrix T *.

The convergence of QL algorithm with shifts for symmetric tridiagonal matrix is discussed and a sufficient condition is given by which shifts are to be chosen to make sure that the top-left diagonal elements converges to an eigenvalue of the matrix.

In this paper, for inverse eigenproblems with given four eigenvalues and eigenvector are considered and are given some necessary and sufficient conditions for the uniqueness of the solution.

Based on the other earlier works as shown in reference and the characteristics of the elements of an irreducibly and weakly diagonally dominant matrix, the row elements of the complex matrix A are divided into three parts, then the module of the elements of each and every part are summed up to obtain the three values α_i, β_i, and γ_i.