Nonnegative matrices with prescribed extremal singular values

  • Authors:

  • Emedin Montaño;Mario Salas;Ricardo L. Soto

  • Affiliations:

  • Departamento de Matemáticas, Universidad Católica del Norte, Casilla 1280, Antofagasta, Chile;Departamento de Matemáticas, Universidad Católica del Norte, Casilla 1280, Antofagasta, Chile;Departamento de Matemáticas, Universidad Católica del Norte, Casilla 1280, Antofagasta, Chile

  • Venue:
  • Computers & Mathematics with Applications
  • Year:
  • 2008

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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 @s"1^(^j^) and @s"j^(^j^),j=1,...,n, we construct an nxn nonnegative bidiagonal matrix B and an nxn nonnegative semi-bordered diagonal matrix C, such that @s"1^(^j^) and @s"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 nxn nonnegative matrix with prescribed singular values @s"1=...=@s"n.