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