Nonnegative matrices with prescribed extremal singular values |
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Authors: | Emedin Montao Mario Salas Ricardo L Soto |
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Affiliation: | aDepartamento de Matemáticas, Universidad Católica del Norte, Casilla 1280, Antofagasta, Chile |
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Abstract: | 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. |
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Keywords: | Singular values Nonnegative matrices |
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