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

     

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• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 38, Nº. 4, 2019, págs. 811-828
• Idioma: inglés
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• 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.