Nonnegative matrices with prescribed extremal singular values

We consider the problem of constructing nonnegative matrices with prescribed extremal singular values. In particular, given 2n−1 real numbers and , we construct an n×n nonnegative bidiagonal matrix B and an n×n nonnegative semi-bordered diagonal matrix C, such that and are, respectively, the minimal and the maximal singular values of certain submatrices Bj and Cj of B and C, respectively. By using a singular value perturbation result, we also construct an n×n nonnegative matrix with prescribed singular values σ1≥ ≥σn