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On the inverse eigenproblem for symmetric and nonsymmetric arrowhead matrices

  • Pickmann Soto, Hubert Rohner [1] ; Arela Pérez, Susana [1] ; Egaña Arancibia, Juan Carlos [2] ; Carrasco Olivera, Dante [3]
    1. [1] Universidad de Tarapacá

      Universidad de Tarapacá

      Arica, Chile

    2. [2] Universidad Católica del Norte

      Universidad Católica del Norte

      Antofagasta, Chile

    3. [3] Universidad del Bío-Bío

      Universidad del Bío-Bío

      Comuna de Concepción, Chile

  • Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 38, Nº. 4, 2019, págs. 811-828
  • Idioma: inglés
  • DOI: 10.22199/issn.0717-6279-2019-04-0053
  • Enlaces
  • Resumen
    • We present a new construction of a symmetric arrow matrix from a particular spectral information: let λ1(n) be the minimal eigenvalue of the matrix and λj(j) ,j=1,2,...,n the maximales eigenvalues of all leading principal submatrices of the matrix. We use such a procedure the to construct a nonsymmetric arrow matrix from the same spectral information next to an eigenvector x(n)=(x1,x2, ,…,xn), so that (x(n),λn(n)) is an eigenpair of the matrix. Moreover our results generate an algorithmic procedure to compute a solution matrix.

             

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