Construction of Lefkovitch and doubly Lefkovitch matrices with maximal eigenvalues and some diagonal elements prescribed

This article considers two inverse eigenvalue problems for Lefkovitch and doubly Lefkovitch matrices. The problems consist of constructing these matrices from the maximal eigenvalues of all its leading principal submatrices, eigenvectors associated with some of these eigenvalues, and some diagonal entries. We give sufficient conditions for the existence of such matrices. In particular, when the matrices have constant diagonal entries. In addition, we provide numerical examples to show the results obtained.