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 2 n ? 1 real numbers ? 1 ( j ) and ? j ( j ) , j = 1 ,  , n , we construct an nn n  n nonnegative bidiagonal matrix B B and an nn n  n nonnegative semi-bordered diagonal matrix C C , such that ? 1 ( j ) and ? j ( j ) are, respectively, the minimal and the maximal singular values of certain submatrices Bj B j and Cj C j of B B and C C , respectively. By using a singular value perturbation result, we also construct an nn n  n nonnegative matrix with prescribed singular values ?1????n ? 1 ? ? ? ? n .
nonnegative matrices singular values