Resumen de On the inverse eigenproblem for symmetric and nonsymmetric arrowhead matrices

Hubert Rohner Pickmann Soto, Susana Arela Pérez, Juan Egaña Arancibia, Dante Carrasco Olivera

• We present a new construction of a symmetric arrow matrix from a particular spectral information: let λ1(n) be the minimal eigenvalue of the matrix and λj(j) ,j=1,2,...,n the maximales eigenvalues of all leading principal submatrices of the matrix. We use such a procedure the to construct a nonsymmetric arrow matrix from the same spectral information next 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.