Relevant bibliographies by topics / Matrix Analysis and Positivity

Academic literature on the topic 'Matrix Analysis and Positivity'

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Published: 6 September 2023

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Journal articles on the topic "Matrix Analysis and Positivity"

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Bhatia, Rajendra, and Ludwig Elsner. "Positivity Preserving Hadamard Matrix Functions." Positivity 11, no. 4 (September 26, 2007): 583–88. http://dx.doi.org/10.1007/s11117-007-2104-8.

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Bernik, Janez, Mitja Mastnak, and Heydar Radjavi. "Positivity and matrix semigroups." Linear Algebra and its Applications 434, no. 3 (February 2011): 801–12. http://dx.doi.org/10.1016/j.laa.2010.09.045.

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ter Horst, S., and A. van der Merwe. "Linear matrix maps for which positivity and complete positivity coincide." Linear Algebra and its Applications 628 (November 2021): 140–81. http://dx.doi.org/10.1016/j.laa.2021.07.007.

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Mørken, Knut M. "On Total Positivity of the Discrete Spline Collocation Matrix." Journal of Approximation Theory 84, no. 3 (March 1996): 247–64. http://dx.doi.org/10.1006/jath.1996.0018.

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Gross, Kenneth I., and Donald St P. Richards. "Total positivity, spherical series, and hypergeometric functions of matrix argument." Journal of Approximation Theory 59, no. 2 (November 1989): 224–46. http://dx.doi.org/10.1016/0021-9045(89)90153-6.

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Horváth, Zoltán. "On the positivity of matrix-vector products." Linear Algebra and its Applications 393 (December 2004): 253–58. http://dx.doi.org/10.1016/j.laa.2004.03.012.

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Melkman, Avraham A. "Another Proof of the Total Positivity of the Discrete Spline Collocation Matrix." Journal of Approximation Theory 84, no. 3 (March 1996): 265–73. http://dx.doi.org/10.1006/jath.1996.0019.

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Johnson, Charles R., and Sivaram K. Narayan. "When the positivity of the leading principal minors implies the positivity of all principal minors of a matrix." Linear Algebra and its Applications 439, no. 10 (November 2013): 2934–47. http://dx.doi.org/10.1016/j.laa.2013.08.017.

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Habel, Azza F., Rabeb M. Ghali, Hanen Bouaziz, Amira Daldoul, Mariem Hadj-Ahmed, Amina Mokrani, Sonia Zaied, et al. "Common matrix metalloproteinase-2 gene variants and altered susceptibility to breast cancer and associated features in Tunisian women." Tumor Biology 41, no. 4 (April 2019): 101042831984574. http://dx.doi.org/10.1177/1010428319845749.

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A role for matrix metalloproteinase polymorphisms in breast cancer development and progression was proposed, but with inconclusive results. We assessed the relation of matrix metalloproteinase-2 variants with breast cancer and related phenotypes in Tunisians. This case-control retrospective study involved 430 women with breast cancer and 498 healthy controls. Genotyping of matrix metalloproteinase-2 rs243866, rs243865, rs243864, and rs2285053 was analyzed by allelic exclusion. The minor allele frequency of rs2285053 was significantly lower in women with breast cancer cases as compared to control women; minor allele frequencies of the remaining single-nucleotide polymorphisms were similar between cases and control women. The distribution of rs243865 and rs2285053 genotypes was significantly different between breast cancer patients and control subjects. This persisted when key covariates were controlled for. None of the matrix metalloproteinase-2 variants were associated with estrogen receptor positivity, progesterone receptor positivity, or with double estrogen receptor–progesterone receptor positivity in breast cancer patients. Matrix metalloproteinase-2 rs243866, rs243865, and rs243864 were positively associated with menstrual irregularity and histological type, while rs243866 and rs2285053 were negatively associated with menarche and nodal status. In addition, rs2285053 was negatively associated with triple negativity, tumor size, distance metastasis, molecular type, and chemotherapy. Haploview analysis revealed high linkage disequilibrium between matrix metalloproteinase-2 variants. Four-locus Haploview analysis identified haplotypes GCTT and GTTC to be negatively associated with breast cancer, which remained statistically after controlling for key covariates. Matrix metalloproteinase-2 alleles and genotypes, along with four-locus haplotypes, are related to reduced susceptibility to breast cancer in Tunisian women, suggesting a protective effect.
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Osada, Hirofumi. "Positivity of the self-diffusion matrix of interacting Brownian particles with hard core." Probability Theory and Related Fields 112, no. 1 (September 17, 1998): 53–90. http://dx.doi.org/10.1007/s004400050183.

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Dissertations / Theses on the topic "Matrix Analysis and Positivity"

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Lecharlier, Loïc. "Blind inverse imaging with positivity constraints." Doctoral thesis, Universite Libre de Bruxelles, 2014. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/209240.

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Dans les problèmes inverses en imagerie, on suppose généralement connu l’opérateur ou matrice décrivant le système de formation de l’image. De façon équivalente pour un système linéaire, on suppose connue sa réponse impulsionnelle. Toutefois, ceci n’est pas une hypothèse réaliste pour de nombreuses applications pratiques pour lesquelles cet opérateur n’est en fait pas connu (ou n’est connu qu’approximativement). On a alors affaire à un problème d’inversion dite “aveugle”. Dans le cas de systèmes invariants par translation, on parle de “déconvolution aveugle” car à la fois l’image ou objet de départ et la réponse impulsionnelle doivent être estimées à partir de la seule image observée qui résulte d’une convolution et est affectée d’erreurs de mesure. Ce problème est notoirement difficile et pour pallier les ambiguïtés et les instabilités numériques inhérentes à ce type d’inversions, il faut recourir à des informations ou contraintes supplémentaires, telles que la positivité qui s’est avérée un levier de stabilisation puissant dans les problèmes d’imagerie non aveugle. La thèse propose de nouveaux algorithmes d’inversion aveugle dans un cadre discret ou discrétisé, en supposant que l’image inconnue, la matrice à inverser et les données sont positives. Le problème est formulé comme un problème d’optimisation (non convexe) où le terme d’attache aux données à minimiser, modélisant soit le cas de données de type Poisson (divergence de Kullback-Leibler) ou affectées de bruit gaussien (moindres carrés), est augmenté par des termes de pénalité sur les inconnues du problème. La stratégie d’optimisation consiste en des ajustements alternés de l’image à reconstruire et de la matrice à inverser qui sont de type multiplicatif et résultent de la minimisation de fonctions coût “surrogées” valables dans le cas positif. Le cadre assez général permet d’utiliser plusieurs types de pénalités, y compris sur la variation totale (lissée) de l’image. Une normalisation éventuelle de la réponse impulsionnelle ou de la matrice est également prévue à chaque itération. Des résultats de convergence pour ces algorithmes sont établis dans la thèse, tant en ce qui concerne la décroissance des fonctions coût que la convergence de la suite des itérés vers un point stationnaire. La méthodologie proposée est validée avec succès par des simulations numériques relatives à différentes applications telle que la déconvolution aveugle d'images en astronomie, la factorisation en matrices positives pour l’imagerie hyperspectrale et la déconvolution de densités en statistique.
Doctorat en Sciences
info:eu-repo/semantics/nonPublished
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Fortmann, Joshua. "Domestic Violence as a Risk Factor in HIV Positivity: An Analysis of Mozambican Women." Digital Commons @ East Tennessee State University, 2021. https://dc.etsu.edu/asrf/2021/presentations/11.

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Domestic violence has long been studied as a factor in health issues, specifically chronic illness and mental health issues. However, less research has been conducted concerning domestic violence as a risk factor for certain infectious diseases. Mozambique has alarmingly high rates of both domestic violence and human immunodeficiency virus (HIV) infections. The object of this research is to ascertain if there is link between women who suffer from domestic violence and risk of being HIV positive. The data used for this analysis was obtained from a 2018 survey conducted in Mozambique by the Department of Health Surveys (DHS). The data was cleaned to remove any observations that did not contain responses to relevant questions surrounding domestic violence and HIV positivity. The final population used for analysis was 2125 individuals. During analysis, age was identified as a possible confounder, and was included in analysis as well as in the final logistic model. A chi squared test was performed which indicated that a relationship exists between Domestic Violence and HIV Positivity (p=.0003). A second chi squared test also indicated a relationship between Age and HIV Positivity (p=
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Chang, Xiao-Wen. "Perturbation analysis of some matrix factorizations." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1997. http://www.collectionscanada.ca/obj/s4/f2/dsk2/tape16/PQDD_0023/NQ29906.pdf.

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Chang, Xiao-Wen 1963. "Pertubation analysis of some matrix factorizations." Thesis, McGill University, 1997. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=41999.

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Matrix factorizations are among the most important and basic tools in numerical linear algebra. Perturbation analyses of matrix factorizations are not only important in their own right, but also useful in many applications, e.g. in estimation, control and statistics. The aim of such analyses is to show what effects changes in the data will have on the factors. This thesis is concerned with developing new general purpose perturbation analyses, and applying them to the Cholesky, QR and LU factorizations, and the Cholesky downdating problem.
We develop a new approach, the so called 'matrix-vector equation' approach, to obtain sharp results and true condition numbers for the above problems. Our perturbation bounds give significant improvements on previous results, and could not be sharper. Also we use the so called 'matrix equation' approach originated by G. W. Stewart to derive perturbation bounds that are usually weaker but easier to interpret. This approach allows efficient computation of satisfactory estimates for the true condition numbers derived by our approach. The combination of these two approaches gives a powerful understanding of these problems. Although first-order perturbation bounds are satisfactory for all but the most delicate work, we also give some rigorous perturbation bounds for some factorizations.
We show that the condition of many such factorizations is significantly improved by the standard pivoting strategies (except the L factor in the LU factorization), and provide firmly based theoretical explanations as to why this is so. This extremely important information is very useful for designing more reliable matrix algorithms.
Our approach is a powerful general tool, and appears to be applicable to the perturbation analysis of any matrix factorization.
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El, Zant Samer. "Google matrix analysis of Wikipedia networks." Thesis, Toulouse, INPT, 2018. http://www.theses.fr/2018INPT0046/document.

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Cette thèse s’intéresse à l’analyse du réseau dirigé extrait de la structure des hyperliens de Wikipédia. Notre objectif est de mesurer les interactions liant un sous-ensemble de pages du réseau Wikipédia. Par conséquent, nous proposons de tirer parti d’une nouvelle représentation matricielle appelée matrice réduite de Google ou "reduced Google Matrix". Cette matrice réduite de Google (GR) est définie pour un sous-ensemble de pages donné (c-à-d un réseau réduit).Comme pour la matrice de Google standard, un composant de GR capture la probabilité que deux noeuds du réseau réduit soient directement connectés dans le réseau complet. Une des particularités de GR est l’existence d’un autre composant qui explique la probabilité d’avoir deux noeuds indirectement connectés à travers tous les chemins possibles du réseau entier. Dans cette thèse, les résultats de notre étude de cas nous montrent que GR offre une représentation fiable des liens directs et indirects (cachés). Nous montrons que l’analyse de GR est complémentaire à l’analyse de "PageRank" et peut être exploitée pour étudier l’influence d’une variation de lien sur le reste de la structure du réseau. Les études de cas sont basées sur des réseaux Wikipédia provenant de différentes éditions linguistiques. Les interactions entre plusieurs groupes d’intérêt ont été étudiées en détail : peintres, pays et groupes terroristes. Pour chaque étude, un réseau réduit a été construit. Les interactions directes et indirectes ont été analysées et confrontées à des faits historiques, géopolitiques ou scientifiques. Une analyse de sensibilité est réalisée afin de comprendre l’influence des liens dans chaque groupe sur d’autres noeuds (ex : les pays dans notre cas). Notre analyse montre qu’il est possible d’extraire des interactions précieuses entre les peintres, les pays et les groupes terroristes. On retrouve par exemple, dans le réseau de peintre sissu de GR, un regroupement des artistes par grand mouvement de l’histoire de la peinture. Les interactions bien connues entre les grands pays de l’UE ou dans le monde entier sont également soulignées/mentionnées dans nos résultats. De même, le réseau de groupes terroristes présente des liens pertinents en ligne avec leur idéologie ou leurs relations historiques ou géopolitiques.Nous concluons cette étude en montrant que l’analyse réduite de la matrice de Google est une nouvelle méthode d’analyse puissante pour les grands réseaux dirigés. Nous affirmons que cette approche pourra aussi bien s’appliquer à des données représentées sous la forme de graphes dynamiques. Cette approche offre de nouvelles possibilités permettant une analyse efficace des interactions d’un groupe de noeuds enfoui dans un grand réseau dirigé
This thesis concentrates on the analysis of the large directed network representation of Wikipedia.Wikipedia stores valuable fine-grained dependencies among articles by linking webpages togetherfor diverse types of interactions. Our focus is to capture fine-grained and realistic interactionsbetween a subset of webpages in this Wikipedia network. Therefore, we propose to leverage anovel Google matrix representation of the network called the reduced Google matrix. This reducedGoogle matrix (GR) is derived for the subset of webpages of interest (i.e. the reduced network). Asfor the regular Google matrix, one component of GR captures the probability of two nodes of thereduced network to be directly connected in the full network. But unique to GR, anothercomponent accounts for the probability of having both nodes indirectly connected through allpossible paths in the full network. In this thesis, we demonstrate with several case studies that GRoffers a reliable and meaningful representation of direct and indirect (hidden) links of the reducednetwork. We show that GR analysis is complementary to the well-known PageRank analysis andcan be leveraged to study the influence of a link variation on the rest of the network structure.Case studies are based on Wikipedia networks originating from different language editions.Interactions between several groups of interest are studied in details: painters, countries andterrorist groups. For each study, a reduced network is built, direct and indirect interactions areanalyzed and confronted to historical, geopolitical or scientific facts. A sensitivity analysis isconducted to understand the influence of the ties in each group on other nodes (e.g. countries inour case). From our analysis, we show that it is possible to extract valuable interactions betweenpainters, countries or terrorist groups. Network of painters with GR capture art historical fact sucha painting movement classification. Well-known interactions of countries between major EUcountries or worldwide are underlined as well in our results. Similarly, networks of terrorist groupsshow relevant ties in line with their objective or their historical or geopolitical relationships. Weconclude this study by showing that the reduced Google matrix analysis is a novel powerfulanalysis method for large directed networks. We argue that this approach can find as well usefulapplication for different types of datasets constituted by the exchange of dynamic content. Thisapproach offers new possibilities to analyze effective interactions in a group of nodes embedded ina large directed network
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Diar, Fares Sonja. "All is well : An analysis of positivity through adjectives in two contemporary New Age self-help books." Thesis, Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, 2018. http://urn.kb.se/resolve?urn=urn:nbn:se:mdh:diva-40144.

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Self-help counselling is an important industry that not only influences its immediate users’ behavior but also society and social behaviors more generally. Since New Ageis a main branch of self-help, and since positivity is a dominant concept in (New Age) self-help discourse, it is worth analyzing how positivity might be achieved in terms of language use. The present study investigates whether the adjectives in a couple of New Age publications contribute to communicating positivity and, if yes, how. What adjectives are used and how can they be categorized in terms of positive, negative, neutral or undetermined connotations as well as semantic prosody? The findings support the hypothesis that the use of “positive adjectives” (Rozin, Berman & Royzman, 2010, p. 536) is what helps to make New Age self-help books convey a positive spirit.
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Barnett, John D. (John Derek) 1970. "Convex matrix factorization for gene expression analysis." Thesis, Massachusetts Institute of Technology, 2004. http://hdl.handle.net/1721.1/30098.

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Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2004.
Includes bibliographical references (p. 68-71).
A method is proposed for gene expression analysis relying upon convex matrix factorization (CMF). In CMF, one of the matrix factors has a convexity constraint, that is, each row is nonnegative and sums to one, and hence can be interpreted as a probability distribution. This is motivated biologically by expression data resulting from a mixture of different cell types. This thesis investigates implementing CMF with various constraints applied to the expression matrix, and applies the technique to a problem in analysis of the cell cycle and two problems in cancer classification.
by John D. Barnett.
S.M.
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Lee, Shi-Wei. "Analysis of Composite Laminates with Matrix Cracks." Thesis, Virginia Tech, 1987. http://hdl.handle.net/10919/45539.

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Analysis of the effects of matrix cracking on composite laminates is a well-known problem which has attracted considerable attention for the past decade. An approximate analytical solution is introduced in this thesis to study this type of problem. The subjects of primary concern are the degradation of effective laminate properties, such as axial stiffness, Poisson's ratio, shear modulus, and coefficient of thermal expansion, as a function of crack density and the axial stress redistribution due to the existence of matrix cracks. Both transverse cracks (2-D problem) and cross (transverse and longitudinal) cracks (3-D problem) are studied. Results for graphite/epoxy cross-ply laminates are presented and compared to those of other approaches. Some other materials, for instance, glass/epoxy, are also studied. The results and comparisons will appear where appropriate. In general, the agreement between the results of the present analysis and those of other approaches, in particular, the finite element method, is good for the lower crack density. The present study shows that Poisson's ratio may be a good indicator of the degree of damage for a cracked laminate.
Master of Science
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Vaandrager, Paul. "Jost-matrix analysis of nuclear scattering data." Thesis, University of Pretoria, 2020. http://hdl.handle.net/2263/75605.

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The analysis of scattering data is usually done by fitting the S-matrix at real experimental energies. An analytic continuation to complex and negative energies must then be performed to locate possible resonances and bound states, which correspond to poles of the S-matrix. Difficulties in the analytic continuation arise since the S-matrix is energy dependent via the momentum, k and the Sommerfeld parameter, η, which makes it multi-valued. In order to circumvent these difficulties, in this work, the S-matrix is written in a semi-analytic form in terms of the Jost matrices, which can be given as a product of known functions dependent on k and η, and unknown functions that are entire and singled-valued in energy. The unknown functions are approximated by truncated Taylor series where the expansion coefficients serve as the data-fitting parameters. The proper analytic structure of the S-matrix is thus maintained. This method is successfully tested with data generated by a model scattering potential. It is then applied to α12C scattering, where resonances of 16O in the quantum states Jρ =0+, 1−, 2+, 3−, and 4+ are located. The parameters of these resonances are accurately determined, as well as the corresponding S-matrix residues and Asymptotic Normalisation Coefficients, relevant to astrophysics. The method is also applied to dα scattering to determine the bound and resonance state parameters, corresponding S-matrix residues and Asymptotic Normalisation Coefficients of 6Li in the 1+, 2+, 3+, 2−, and 3− states.
Thesis (PhD)--University of Pretoria, 2020.
National Research Foundation (NRF)
Physics
PhD
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Knox, Andrew Ramsay. "Design and analysis of the magnetic matrix display." Connect to electronic version, 2000. http://hdl.handle.net/1905/187.

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Books on the topic "Matrix Analysis and Positivity"

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R, Johnson Charles, ed. Matrix analysis. Cambridge [Cambridgeshire]: Cambridge University Press, 1985.

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Bhatia, Rajendra. Matrix Analysis. New York, NY: Springer New York, 1997. http://dx.doi.org/10.1007/978-1-4612-0653-8.

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Horn, Roger A. Matrix analysis. Cambridge [Cambridgeshire]: Cambridge University Press, 1990.

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Horn, Roger A. Matrix analysis. 2nd ed. Cambridge: Cambridge University Press, 2012.

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Bhatia, Rajendra. Matrix analysis. New York: Springer, 1997.

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H, Gallagher Richard, and Ziemian Ronald D, eds. Matrix structural analysis. 2nd ed. New York: John Wiley, 2000.

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Matrix structural analysis. Boston: PWS-Kent Pub. Co., 1989.

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Varga, Richard S. Matrix Iterative Analysis. Berlin, Heidelberg: Springer Berlin Heidelberg, 2000. http://dx.doi.org/10.1007/978-3-642-05156-2.

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Varga, Richard S. Matrix iterative analysis. 2nd ed. Berlin: Springer Verlag, 2000.

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B, Nelson Richard, ed. Matrix structural analysis. New York: J. Wiley, 1997.

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Book chapters on the topic "Matrix Analysis and Positivity"

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Lefaucheux, Engel, Joël Ouaknine, David Purser, and Mohammadamin Sharifi. "Model Checking Linear Dynamical Systems under Floating-point Rounding." In Tools and Algorithms for the Construction and Analysis of Systems, 47–65. Cham: Springer Nature Switzerland, 2023. http://dx.doi.org/10.1007/978-3-031-30823-9_3.

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AbstractWe consider linear dynamical systems under floating-point rounding. In these systems, a matrix is repeatedly applied to a vector, but the numbers are rounded into floating-point representation after each step (i.e., stored as a fixed-precision mantissa and an exponent). The approach more faithfully models realistic implementations of linear loops, compared to the exact arbitrary-precision setting often employed in the study of linear dynamical systems.Our results are twofold: We show that for non-negative matrices there is a special structure to the sequence of vectors generated by the system: the mantissas are periodic and the exponents grow linearly. We leverage this to show decidability of $$\omega $$ ω -regular temporal model checking against semialgebraic predicates. This contrasts with the unrounded setting, where even the non-negative case encompasses the long-standing open Skolem and Positivity problems.On the other hand, when negative numbers are allowed in the matrix, we show that the reachability problem is undecidable by encoding a two-counter machine. Again, this is in contrast with the unrounded setting where point-to-point reachability is known to be decidable in polynomial time.
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Gesztesy, Fritz, and Michael M. H. Pang. "On Positivity Preserving, Translation Invariant Operators in $$ \mathit L^p (\mathbb R^n)^m $$." In Analysis as a Tool in Mathematical Physics, 335–50. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-31531-3_19.

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Borawski, Kamil. "Analysis of the Positivity of Descriptor Continuous-Time Linear Systems by the Use of Drazin Inverse Matrix Method." In Advances in Intelligent Systems and Computing, 172–82. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-77179-3_16.

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Chesi, Graziano, Andrea Garulli, Alberto Tesi, and Antonio Vicino. "Positivity Gap." In Homogeneous Polynomial Forms for Robustness Analysis of Uncertain Systems, 39–61. London: Springer London, 2009. http://dx.doi.org/10.1007/978-1-84882-781-3_2.

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Dancer, E. N. "Positivity of Maps and Applications." In Topological Nonlinear Analysis, 303–40. Boston, MA: Birkhäuser Boston, 1995. http://dx.doi.org/10.1007/978-1-4612-2570-6_4.

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Fu, Siqi. "Positivity in the ∂¯-Neumann Problem." In Handbook of Complex Analysis, 89–132. Boca Raton: Chapman and Hall/CRC, 2022. http://dx.doi.org/10.1201/9781315160658-5.

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Jia, Rong-Qing. "Total Positivity and Nonlinear Analysis." In Total Positivity and Its Applications, 403–27. Dordrecht: Springer Netherlands, 1996. http://dx.doi.org/10.1007/978-94-015-8674-0_19.

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Fu, Siqi. "Positivity of the $$ \bar \partial $$ -Neumann Laplacian." In Complex Analysis, 145–58. Basel: Birkhäuser Basel, 2010. http://dx.doi.org/10.1007/978-3-0346-0009-5_8.

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Gladwell, G. M. L. "Matrix Analysis." In Inverse problems in vibration, 1–17. Dordrecht: Springer Netherlands, 1986. http://dx.doi.org/10.1007/978-94-015-1178-0_1.

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Esfandiari, Ramin S., and Bei Lu. "Matrix Analysis." In Modeling and Analysis of Dynamic Systems, 75–103. Third edition. | Boca Raton : Taylor & Francis, CRC Press, 2018.: CRC Press, 2018. http://dx.doi.org/10.1201/b22138-3.

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Conference papers on the topic "Matrix Analysis and Positivity"

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de Oliveira, Mauricio C., Ricardo C. L. F. Oliveira, and Pedro L. D. Peres. "Schur stability of polytopic systems through positivity analysis of matrix-valued polynomials." In 2007 46th IEEE Conference on Decision and Control. IEEE, 2007. http://dx.doi.org/10.1109/cdc.2007.4434750.

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Yedavalli, Rama K., and Nagini Devarakonda. "Determination of Most Desirable Nominal Closed Loop State Space System via Qualitative Ecological Principles." In ASME 2014 Dynamic Systems and Control Conference. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/dscc2014-6181.

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This paper addresses the issue of determining the most desirable ‘Nominal Closed Loop Matrix’ structure in linear state space systems, by combining the concepts of ‘Quantitative Robustness’ and ‘Qualitative Robustness’. The qualitative robustness measure is based on the nature of interactions and interconnections of the system. The quantitative robustness is based on the nature of eigenvalue/eigenvector structure of the system. This type of analysis from both viewpoints sheds considerable insight on the desirable nominal system in engineering applications. Using these concepts it is shown that a specific quantitative set of matrices labeled ‘Quantitative Ecological Stable (QES) Matrices’ have features which qualify them as the most desirable nominal closed loop system matrices. Thus in this paper, we expand on the special features of the determinant of a matrix in terms of self-regulation, interactions and interconnections and specialize these features to the class of ‘Quantitative Ecological Stable (QES)’ matrices and show that for checking its Hurwitz stability, it is sufficient to check the positivity of only the constant coefficient of the characteristic polynomial of a matrix in a higher dimensional ‘Kronecker’ space. In addition, it is shown that these matrices possess the most attractive property among any matrix class, namely that their Determinants possess convexity property. Establishment of this optimal nominal closed loop system matrix structure paves the way for designing controllers which qualify as robust controllers for linear systems with real parameter uncertainty. The proposed concepts are illustrated with many useful examples.
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Artru, X. "Classical positivity, quantum positivity and entanglement of a multi-partite density matrix, with the example of polarized reactions." In THE 8TH INTERNATIONAL CONFERENCE ON PROGRESS IN THEORETICAL PHYSICS (ICPTP 2011). AIP, 2012. http://dx.doi.org/10.1063/1.4715425.

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Iwasaki, Masashi, and Yoshimasa Nakamura. "Positivity and Stability of the dLV Algorithm for Computing Matrix Singular Values." In Second International Conference on Informatics Research for Development of Knowledge Society Infrastructure (ICKS'07). IEEE, 2007. http://dx.doi.org/10.1109/icks.2007.22.

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Renganarayana, Lakshminarayanan, and Sanjay Rajopadhye. "Positivity, posynomials and tile size selection." In 2008 SC - International Conference for High Performance Computing, Networking, Storage and Analysis. IEEE, 2008. http://dx.doi.org/10.1109/sc.2008.5213293.

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Nalbant, Nese, and Yasar Sozen. "The positivity of differential operator with nonlocal boundary conditions." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2012: International Conference of Numerical Analysis and Applied Mathematics. AIP, 2012. http://dx.doi.org/10.1063/1.4756198.

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Ashyralyev, Allaberen, and Fatih Sabahattin Tetikoğlu. "The positivity of the differential operator with periodic conditions." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2012: International Conference of Numerical Analysis and Applied Mathematics. AIP, 2012. http://dx.doi.org/10.1063/1.4756200.

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Semenova, Galina E. "Positivity of elliptic difference operators and its applications." In FIRST INTERNATIONAL CONFERENCE ON ANALYSIS AND APPLIED MATHEMATICS: ICAAM 2012. AIP, 2012. http://dx.doi.org/10.1063/1.4747683.

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Ashyralyev, Allaberen, Sema Kaplan, Yasar Sozen, Theodore E. Simos, George Psihoyios, Ch Tsitouras, and Zacharias Anastassi. "Positivity of Two-Dimensional Elliptic Differential Operators with Nonlocal Conditions." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2011: International Conference on Numerical Analysis and Applied Mathematics. AIP, 2011. http://dx.doi.org/10.1063/1.3636803.

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Gao, Haichao, Wei Dong, and Linli Ma. "Positivity and stability analysis of positive discrete-time descriptor systems." In 2016 Chinese Control and Decision Conference (CCDC). IEEE, 2016. http://dx.doi.org/10.1109/ccdc.2016.7531126.

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Reports on the topic "Matrix Analysis and Positivity"

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Hurtubise, R. J. Solid-matrix luminescence analysis. Office of Scientific and Technical Information (OSTI), January 1993. http://dx.doi.org/10.2172/6568645.

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Caswell, Hal. Matrix Methods for Population Analysis. Fort Belvoir, VA: Defense Technical Information Center, January 1997. http://dx.doi.org/10.21236/ada330118.

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Kailath, Thomas. Recursive Analysis of Matrix Scattering Functions. Fort Belvoir, VA: Defense Technical Information Center, December 1993. http://dx.doi.org/10.21236/ada277264.

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Robert J. Hurtubise. Solid-Matrix Luminescence Analysis and Coupling Solid-Matrix Luminescence with Separation Methodology. Office of Scientific and Technical Information (OSTI), August 2007. http://dx.doi.org/10.2172/1009088.

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Hurtubise, Robert J. Solid-Matrix Luminescence Analysis and Coupling Solid-Matrix Luminescence with Separation Methodology. Office of Scientific and Technical Information (OSTI), June 2004. http://dx.doi.org/10.2172/838042.

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Bane, Karl LF. SCATTERING MATRIX ANALYSIS OF THE NLC ACCELERATING STRUCTURE. Office of Scientific and Technical Information (OSTI), April 1999. http://dx.doi.org/10.2172/10045.

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Yu, Li Hua. Analysis of Nonlinear Dynamics by Square Matrix Method. Office of Scientific and Technical Information (OSTI), July 2016. http://dx.doi.org/10.2172/1340371.

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Wang, A. S. Fracture Analysis of Matrix Cracking in Laminated Composites. Fort Belvoir, VA: Defense Technical Information Center, January 1985. http://dx.doi.org/10.21236/ada170486.

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Wolski, A., J. Nelson, M. Ross, M. Woodley, and S. Mishra. Analysis of KEK-ATF Optics And Coupling Using Orbit Response Matrix Analysis. Office of Scientific and Technical Information (OSTI), October 2006. http://dx.doi.org/10.2172/893293.

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Wolski, A., J. Nelson, M. Ross, M. Woodley, and S. Mishra. Analysis of KEK-ATF optics and coupling using orbit response matrix analysis. Office of Scientific and Technical Information (OSTI), January 2004. http://dx.doi.org/10.2172/898407.

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