On the inverse eigenproblem for symmetric and nonsymmetric arrowhead matrices.

We present a new construction of a symmetric arrow matrix from a particular spectral information: let ɻ(n) be the minimal eigenvalue of the matrix and ɻ®, 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), ɻn(n) is an eigenpair of the matrix. Moreover, our results generate an algorithmic procedure to compute a solution matrix. [ABSTRACT FROM AUTHOR]