Abstract: The following inverse eigenvalue problem for Jacobi matrices is considered: Problem IEP.Given λ,μ∈R(λ<μ and x,y∈Rⁿ,x≠0,y≠0, find n×n Jacobi matrix J such that (λ,x) and (μ,y) are exactly the i-th and j-th (i≠j) eigenpairs of the Jacobi matrix J, respectively. The eigenanalysis of Jacobi matrices is given. The necessary and sufficient condition is obtained for one eigenpair to be exactly the i-th eigenpair of a Jacobi matrix. Some necessary and sufficient conditions for existence of solution of the Problem IEP are given.

Key words: characteristic value, characteristic vector, inverse problem, Jacobi matrix