TY - JOUR AU - Pickmann Soto, Hubert Rohner AU - Arela Pérez, Susana AU - Egaña Arancibia, Juan Carlos AU - Carrasco Olivera, Dante PY - 2019/10/22 Y2 - 2024/03/28 TI - On the inverse eigenproblem for symmetric and nonsymmetric arrowhead matrices JF - Proyecciones (Antofagasta, On line) JA - Proyecciones (Antofagasta, On line) VL - 38 IS - 4 SE - DO - 10.22199/issn.0717-6279-2019-04-0053 UR - https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/3531 SP - 811-828 AB - We present a new construction of a symmetric arrow matrix from a particular spectral information: let λ(n) 1 be the minimal eigenvalue of the matrix and λj (j) , j = 1, 2, . . . , n the maximal eigenvalues of all leading principal submatrices of the matrix. We use such a procedure to construct a nonsymmetric arrow matrix from the same spectral information plus to an eigenvector x(n) = (x1, x2, . . . , xn), so that (x(n), λn (n)) is an eigenpair of the matrix. Moreover, our results generate an algorithmic procedure to compute a solution matrix. ER -