Extremal inverse eigenvalue problem for symmetric doubly arrow matrices
In this paper, we consider the following inverse eigenvalue problem: to construct a real symmetric doubly arrow matrix A from the minimal and maximal eigenvalues of all its leading principal submatrices. The necessary and sufficient condition for the solvability of the problem is derived. We also give a necessary and sufficient condition in order that the constructed matrices can be nonnegative. Our results are constructive and they generate algorithmic procedures to construct such matrices.
inverse eigenvalue problem symmetric doubly arrow matrix nonnegative matrix 15a57 65f15 65f18