A note for the SNIEP in size 5

Producción CientíficaThe purpose of this note is to establish the current state of the knowledge about the SNIEP (symmetric nonnegative inverse eigenvalue problem) in size 5 with just one repeated eigenvalue.Ministerio de Ciencia e Innovación - AEI (grant PGC2018-096446-B-C21)Consejo Superior de Investigaciones Científicas de España (Comisión Interministerial de Ciencia y Tecnología) (PID2021-122501NB-I00

On spectra of weighted graphs of order ≤5

Producción CientíficaThe problem of characterizing the real spectra of weighted graphs is only solved for weighted graphs of order n ≤ 4. We overview these known results, that come from the context of nonnegative matrices, and give a new method to rule out many unresolved spectra of size 5.Ministerio de Economía, Industria y Competitividad ( grant MTM2015-365764-C3-1-P)Universidad de Valladolid (GIR TAMCO

Updating a map of sufficient conditions for the real nonnegative inverse eigenvalue problem

Producción CientíficaThe real nonnegative inverse eigenvalue problem (RNIEP) asks for necessary and sufficient conditions in order that a list of real numbers be the spectrum of a nonnegative real matrix. A number of sufficient conditions for the existence of such a matrix are known. The authors gave in a map of sufficient conditions establishing inclusion relations or independency relations between them. Since then new sufficient conditions for the RNIEP have appeared. In this paper we complete and update the map given in.Fondo Nacional de Desarrollo Científico y Tecnológico de Chile (project 1170313)Ministerio de Economía, Industria y Competitividad - Fondo Europeo de Desarrollo Regional (projects MTM2015-365764-C-1 / MTM2017-85996-R)Junta de Castilla y León (project VA128G18

On universal realizability of spectra

Producción CientíficaA list Λ = {λ1, λ2, . . . , λn} of complex numbers is said to be realizable if it is the spectrum of an entrywise nonnegative matrix. The list Λ is said to be universally realizable (UR) if it is the spectrum of a nonnegative matrix for each possible Jordan canonical form allowed by Λ. It is well known that an n × n nonnegative matrix A is co-spectral to a nonnegative matrix B with constant row sums. In this paper, we extend the co-spectrality between A and B to a similarity between A and B, when the Perron eigenvalue is simple. We also show that if ǫ ≥ 0 and Λ = {λ1, λ2, . . . , λn} is UR, then {λ1 + ǫ, λ2, . . . , λn} is also UR. We give counter-examples for the cases: Λ = {λ1, λ2, . . . , λn} is UR implies {λ1 + ǫ, λ2 − ǫ, λ3, . . . , λn} is UR, and Λ1,Λ2 are UR implies Λ1 ∪ Λ2 is UR.Comisión Nacional de Investigación Científica y Tecnológica - Fondo Nacional de Desarrollo Científico y Tecnológico 1170313Comisión Nacional de Investigación Científica y Tecnológica - PAI 79160002Ministerio de Economía, Industria y Competitividad ( grants MTM2015-365764-C-1 / MTM2017-85996-R))Consejería de Educación de la Junta de Castilla y León (grant VA128G18

Evaluación continua con Quizzes (ECQ)

La evaluación de la experiencia, tanto por parte de los estudiantes como de los profesores, ha sido muy positiva; por ello la propuesta actual es utilizar las Quizzes del programa Wiris para potenciar un mejor y mayor aprendizaje de los estudiantes y facilitar al profesorado una evaluación continua de los mismos. La utilización de Wiris Quizzes facilita la generación de preguntas con una gran aleatoriedad obteniendo un abanico muy amplio de cuestionarios. El tipo de preguntas que pueden crearse es muy diverso, pueden incluirse gráficas y fórmulas generadas con la calculadora y el editor de Wiris. Los cuestionarios tienen una doble utilidad, tanto de autoevaluación del aprendizaje por parte del estudiante, como de evaluación continuada por parte del profesor de los conocimientos alcanzados por los alumnos. Sus resultados permiten comprobar el nivel de conocimientos adquiridos y ayudan al estudiante en el estudio continuado del temario.Departamento de Matemática Aplicad

Ruling Out Certain 5-Spectra for the Symmetric Nonnegative Inverse Eigenvalue Problem

Producción CientíficaA method is developed to show that certain spectra cannot be realized for the S-NIEP. It is applied in the 5-by-5 case to rule out many spectra that were previously unresolved. These are all in the case of 3 positive and 2 negative eigenvalues as all other cases are now resolved. For spectra of the sort we discuss, a diagram is given of the spectra that are excluded here, as well as those trivially realizable, those realizable because of the trace 0 case and those that may also be excluded because of the J–L–L conditions. A small region remains unresolved; it is a very small fraction of the area of those spectra we consider

A map of sufficient conditions for the symmetric nonnegative inverse eigenvalue problem

Producción CientíficaThe symmetric nonnegative inverse eigenvalue problem (SNIEP) asks for necessary and sufficient conditions in order that a list of real numbers be the spectrum of a symmetric nonnegative real matrix. A number of sufficient conditions for the existence of such a matrix are known. In this paper, in order to construct a map of sufficient conditions, we compare these conditions and establish inclusion relations or independence relations between them

Symmetric nonnegative realizability via partitioned majorization

Producción CientíficaA sufficient condition for symmetric nonnegative realizability of a spectrum is given in terms of (weak) majorization of a partition of the negative eigenvalues by a selection of the positive eigenvalues. If there are more than two positive eigenvalues, an additional condition, besides majorization, is needed on the partition. This generalizes observations of Suleˇımanova and Loewy about the cases of one and two positive eigenvalues, respectively. It may be used to provide insight into realizability of 5-element spectra and beyond.Ministerio de Economía, Industria y Competitividad (MTM2015-365764-C-1-P / MTM2010- 19281-C03-01

Guión y práctica de laboratorio. Integrales dobles

Práctica de laboratorio. Integrales doblesDepartamento de Matemática Aplicad

Guión y práctica de laboratorio. Aplicaciones lineales

Práctica de laboratorio. Aplicaciones linealesDepartamento de Matemática Aplicad