On the inverse eigenproblem for symmetric and nonsymmetric arrowhead matrices





Arrow matrices, Symmetric and nonsymmetric matrix, Inverse eigenvalue problem


We present a new construction of a symmetric arrow matrix from a particular spectral information: let λ(n) 1 be the minimal eigenvalue of the matrix and λj (j) , j = 1, 2, . . . , n the maximal eigenvalues of all leading principal submatrices of the matrix. We use such a procedure to construct a nonsymmetric arrow matrix from the same spectral information plus 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.

Author Biographies

H. Pickmann, Universidad de Tarapacá.

Dept. de Matemática.

S. Arela, Universidad de Tarapacá.

Dept. de Matemática.

J. Egaña, Universidad Católica del Norte.

Dept. de Matemáticas.

D. Carrasco, Universidad del Bío-Bío.

Dept de Matemática.


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How to Cite

H. R. Pickmann Soto, S. Arela Pérez, J. C. Egaña Arancibia, and D. Carrasco Olivera, “On the inverse eigenproblem for symmetric and nonsymmetric arrowhead matrices”, Proyecciones (Antofagasta, On line), vol. 38, no. 4, pp. 811-828, Oct. 2019.




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