RT info:eu-repo/semantics/article
T1 Bisymmetric nonnegative Jacobi matrix realizations
A1 Pisonero Pérez, Miriam
A1 Marijuán López, Carlos
A1 Encinas Bachiller, Andrés Marcos
A1 Jiménez, María José
A1 Mitjana, Margarida
K1 Jacobi matrix; non-negative matrix; realization; bisymmetric matrix
AB Within the symmetric inverse eigenvalue problem, the case of bisym-metric Jacobi matrices occupies a central place, since for any strictlymonotone list of n real numbers there exists a unique bisymmetricJacobi matrix realizing the list. Apart from their meaning in severalissues such as physics, mechanics, statistics, to cite some of them, thefamilies of this kind of matrices whose spectrum is known are usedas models for testing the different algorithms to recover the entriesof matrices from spectra data. However, the spectrum is known onlyfor a few families of bisymmetric Jacobi matrices and the examplesmainly refer to the case when the spectrum is given by a linear orquadratic function of the order and of the row index. In the firstpart of this paper, we join all known cases by proving a generalresult about bisymmetric Jacobi realizations of strictly monotonesequences that are quadratic at most. In the second part, we focus onthe non-negative bisymmetric realizations, obtaining new necessaryconditions for a given list to be realized by a non-negative bisymmet-ric Jacobi matrix. The main novelty in our techniques is consideringthe gaps between the eigenvalues instead of focusing on the eigen-values themselves. In the last part of this paper, we explicitly obtainthe bisymmetric realization of any list for order less or equal to 6.
PB Taylor&Francis
SN 0308-1087
YR 2025
FD 2025
LK https://uvadoc.uva.es/handle/10324/79155
UL https://uvadoc.uva.es/handle/10324/79155
LA eng
NO Linear and Multulinear Algebra, Vol 73, n 9, p.1984-2011
NO Producción Científica
DS UVaDOC
RD 01-nov-2025