160782 20251017144551.0 doi 10.3390/axioms14040232 sideral 143970 ART-2025-143970 eng Peña, Juan M. Universidad de Zaragoza (orcid)0000-0002-1340-0666 Eigenvalue Localization for Symmetric Positive Toeplitz Matrices 2025 Access copy available to the general public Unrestricted Given a real symmetric matrix, several inclusion and exclusion intervals containing its eigenvalues can be given. In this paper, for symmetric positive Toeplitz matrices, we provide an inclusion interval and, under an additional hypothesis, we also give two disjoint intervals contained in the previous one and containing all the eigenvalues. Examples are included, showing that these two intervals are necessary and that they can provide precise information on the localization of the eigenvalues. Sufficient conditions for positive definiteness are included. Necessary and sufficient conditions for the total positivity of symmetric positive Toeplitz matrices are presented. A characterization of symmetric totally positive circulant matrices is also obtained. info:eu-repo/grantAgreement/ES/DGA/E41-23R info:eu-repo/grantAgreement/ES/MCIU/PID2022-138569NB-I00 info:eu-repo/grantAgreement/ES/MICINN/RED2022-134176-T info:eu-repo/semantics/openAccess by https://creativecommons.org/licenses/by/4.0/deed.es info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion 2005 595 Universidad de Zaragoza Dpto. Matemática Aplicada Área Matemática Aplicada 14, 4 (2025), 232 [12 pp.] Axioms Axioms 2075-1680 267331 http://zaguan.unizar.es/record/160782/files/texto_completo.pdf Versión publicada 2405849 http://zaguan.unizar.es/record/160782/files/texto_completo.jpg?subformat=icon icon Versión publicada oai:zaguan.unizar.es:160782 articulos driver 2025-10-17-14:11:50 ARTICLE