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In this paper, we deal with Leslie and doubly Leslie matrices of order n. In particular, with the companion and doubly companion matrices. We study three inverse eigenvalues problems which consist of constructing these matrices from the maximal eigenvalues of its all leading principal submatrices. For Leslie and doubly companion matrices, an eigenvector associated with the maximal eigenvalue of the matrix is additionally considered, and for the doubly Leslie matrix also an eigenvector associated with the maximal eigenvalue of leading principal submatrix of order n − 1 is required. We give necessary and sufficient conditions for the existence of a Leslie matrix and a companion matrix, and sufficient conditions for the existence of a doubly Leslie matrix and a doubly companion matrix. Our results are constructive and generate an algorithmic procedure to construct these special kinds of matrices. [ABSTRACT FROM AUTHOR]

In this paper, we give sufficient conditions for the construction of periodic and generalized periodic Jacobi matrices from particular spectral data. For the construction of a periodic Jacobi matrix, the smallest and largest eigenvalues of all its leading principal submatrices, and a prescribed entry are required. For the case of the generalized periodic Jacobi matrix, an eigenvector associated with the largest eigenvalue is additionally considered. The results obtained provide algorithmic procedures that are illustrated in some numerical experiments. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]