The NIEP

The nonnegative inverse eigenvalue problem (NIEP) asks which lists of $n$ complex numbers (counting multiplicity) occur as the eigenvalues of some $n$-by-$n$ entry-wise nonnegative matrix. The NIEP has a long history and is a known hard (perhaps the hardest in matrix analysis?) and sought after problem. Thus, there are many subproblems and relevant results in a variety of directions. We survey most work on the problem and its several variants, with an emphasis on recent results, and include 130 references. The survey is divided into: a) the single eigenvalue problems; b) necessary conditions; c) low dimensional results; d) sufficient conditions; e) appending 0's to achieve realizability; f) the graph NIEP's; g) Perron similarities; and h) the relevance of Jordan structure

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

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

AbstractThe real nonnegative inverse eigenvalue problem (RNIEP) is the problem of determining necessary and sufficient conditions for a list of real numbers Λ to be the spectrum of an entrywise nonnegative 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 independency relations between them

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 with one repeated eigenvalue for the symmetric NIEP

Producción CientíficaHere, prior work, that ruled out certain spectra with two repeated eigenvalues for the 5-by-5 S-NIEP, is extended. Previously unresolved spectra with just one repeated eigenvalue are shown not to occur. The repeat could be either positive or negative, but the two situations are different. In both situations, the prior result with two repeats is a special case.PGC2018-096446-B-C21 (MINECO/FEDER)MTM2017-85996-R (MINECO/ FEDER)Consejería de Educación de la Junta de Castilla y León (Spain) VA128G1

Diagonal dominance and invertibility of matrices

Producción CientíficaA weakly diagonally dominant matrix may or may not be invertible. We characterize, in terms of combinatorial structure and sign pattern when such a matrix is invertible, which is the common case. Examples are given.PGC2018-096446-B-C21 funded by MCIN/ AEI/10.13039/501100011033, “ERDF A way of making Europe”GIR TAAMC from UV