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 λ⁽ⁿ⁾ be the minimal eigenvalue of the matrix and, j = l,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,..., x_n), so that (x⁽ⁿ⁾,) is an eigenpair of the matrix. Moreover, our results generate an algorithmic procedure to compute a solution matrix.