000160782 001__ 160782 000160782 005__ 20251017144551.0 000160782 0247_ $$2doi$$a10.3390/axioms14040232 000160782 0248_ $$2sideral$$a143970 000160782 037__ $$aART-2025-143970 000160782 041__ $$aeng 000160782 100__ $$0(orcid)0000-0002-1340-0666$$aPeña, Juan M.$$uUniversidad de Zaragoza 000160782 245__ $$aEigenvalue Localization for Symmetric Positive Toeplitz Matrices 000160782 260__ $$c2025 000160782 5060_ $$aAccess copy available to the general public$$fUnrestricted 000160782 5203_ $$aGiven 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. 000160782 536__ $$9info:eu-repo/grantAgreement/ES/DGA/E41-23R$$9info:eu-repo/grantAgreement/ES/MCIU/PID2022-138569NB-I00$$9info:eu-repo/grantAgreement/ES/MICINN/RED2022-134176-T 000160782 540__ $$9info:eu-repo/semantics/openAccess$$aby$$uhttps://creativecommons.org/licenses/by/4.0/deed.es 000160782 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/publishedVersion 000160782 7102_ $$12005$$2595$$aUniversidad de Zaragoza$$bDpto. Matemática Aplicada$$cÁrea Matemática Aplicada 000160782 773__ $$g14, 4 (2025), 232 [12 pp.]$$pAxioms$$tAxioms$$x2075-1680 000160782 8564_ $$s267331$$uhttps://zaguan.unizar.es/record/160782/files/texto_completo.pdf$$yVersión publicada 000160782 8564_ $$s2405849$$uhttps://zaguan.unizar.es/record/160782/files/texto_completo.jpg?subformat=icon$$xicon$$yVersión publicada 000160782 909CO $$ooai:zaguan.unizar.es:160782$$particulos$$pdriver 000160782 951__ $$a2025-10-17-14:11:50 000160782 980__ $$aARTICLE