The Uniqueness of Solution to the Inverse Eigenvalue Problem for an Arrow-shaped Generalised Jacobi Matrix

This paper studies the inverse eigenvalue problem for an arrow-shaped generalised Jacobi matrix, inverting matrices through two eigen-pairs. In the paper, the existence and uniqueness of the solution to the problem are discussed, and mathematical expressions as well as a numerical example are given. Finally, the uniqueness theorem of its matrix is established by mathematical derivation.

Inverse eigenvalue problem for Jacobi matrix and nonnegative matrices

In this paper, we present a method for constructing a Jacobi matrix [Formula: see text] using [Formula: see text] known eigenvalues [Formula: see text]. Some conditions are also given under which the constructed matrix is nonnegative and its diagonal entries are specified. Finally, we present a technique for constructing symmetric and nonsymmetric nonnegative matrices by their eigenvalues.