LEADER 03743nam 2200625 450 001 9910483059803321 005 20230427102857.0 010 $a3-030-52815-4 024 7 $a10.1007/978-3-030-52815-7 035 $a(CKB)4100000011938300 035 $a(DE-He213)978-3-030-52815-7 035 $a(MiAaPQ)EBC6627983 035 $a(Au-PeEL)EBL6627983 035 $a(OCoLC)1252706564 035 $a(PPN)255885946 035 $a(EXLCZ)994100000011938300 100 $a20220124d2021 uy 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aAdvanced linear and matrix algebra /$fNathaniel Johnston 205 $a1st ed. 2021. 210 1$aCham, Switzerland :$cSpringer,$d[2021] 210 4$dŠ2021 215 $a1 online resource (XVI, 494 p. 123 illus., 108 illus. in color.) 311 $a3-030-52814-6 320 $aIncludes bibliographical references and index. 327 $aChapter 1: Vector Spaces -- Chapter 2: Matrix Decompositions -- Chapter 3: Tensors and Multilinearity -- Appendix A: Mathematical Preliminaries -- Appendix B: Additional Proofs -- Appendix C: Selected Exercise Solutions. 330 $aThis textbook emphasizes the interplay between algebra and geometry to motivate the study of advanced linear algebra techniques. Matrices and linear transformations are presented as two sides of the same coin, with their connection motivating inquiry throughout the book. Building on a first course in linear algebra, this book offers readers a deeper understanding of abstract structures, matrix decompositions, multilinearity, and tensors. Concepts draw on concrete examples throughout, offering accessible pathways to advanced techniques. Beginning with a study of vector spaces that includes coordinates, isomorphisms, orthogonality, and projections, the book goes on to focus on matrix decompositions. Numerous decompositions are explored, including the Shur, spectral, singular value, and Jordan decompositions. In each case, the author ties the new technique back to familiar ones, to create a coherent set of tools. Tensors and multilinearity complete the book, with a study of the Kronecker product, multilinear transformations, and tensor products. Throughout, ?Extra Topic? sections augment the core content with a wide range of ideas and applications, from the QR and Cholesky decompositions, to matrix-valued linear maps and semidefinite programming. Exercises of all levels accompany each section. Advanced Linear and Matrix Algebra offers students of mathematics, data analysis, and beyond the essential tools and concepts needed for further study. The engaging color presentation and frequent marginal notes showcase the author?s visual approach. A first course in proof-based linear algebra is assumed. An ideal preparation can be found in the author?s companion volume, Introduction to Linear and Matrix Algebra. 606 $aAlgebras, Linear 606 $aMatrices 606 $aĀlgebra lineal$2thub 606 $aMatrius (Matemātica)$2thub 606 $aAlgebra 606 $aĀlgebra lineal$2thub 606 $aMatrius (Matemātica)$2thub 608 $aLlibres electrōnics$2thub 615 0$aAlgebras, Linear. 615 0$aMatrices. 615 7$aĀlgebra lineal 615 7$aMatrius (Matemātica) 615 0$aAlgebra. 615 7$aĀlgebra lineal 615 7$aMatrius (Matemātica) 676 $a512.5 700 $aJohnston$b Nathaniel$0848126 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910483059803321 996 $aAdvanced Linear and Matrix Algebra$91896815 997 $aUNINA LEADER 04991nam 2200469z- 450 001 9910220034403321 005 20210212 035 $a(CKB)3800000000216433 035 $a(oapen)https://directory.doabooks.org/handle/20.500.12854/62617 035 $a(oapen)doab62617 035 $a(EXLCZ)993800000000216433 100 $a20202102d2016 |y 0 101 0 $aeng 135 $aurmn|---annan 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 00$aWhat Determines Social Behavior? Investigating the Role of Emotions, Self-Centered Motives, and Social Norms 210 $cFrontiers Media SA$d2016 215 $a1 online resource (403 p.) 225 1 $aFrontiers Research Topics 311 08$a2-88919-964-9 330 $aHuman behavior and decision making is subject to social and motivational influences such as emotions, norms and self/other regarding preferences. The identification of the neural and psychological mechanisms underlying these factors is a central issue in psychology, behavioral economics and social neuroscience, with important clinical, social, and even political implications. However, despite a continuously growing interest from the scientific community, the processes underlying these factors, as well as their ontogenetic and phylogenetic development, have so far remained elusive. In this Research Topic we collect articles that provide challenging insights and stimulate a fruitful controversy on the question of "what determines social behavior". Indeed, over the last decades, research has shown that introducing a social context to otherwise abstract tasks has diverse effects on social behavior. On the one hand, it may induce individuals to act irrationally, for instance to refuse money, but on the other hand it improves individuals' reasoning, in that formerly difficult abstract problems can be easily solved. These lines of research led to distinct (although not necessarily mutually exclusive) models for socially-driven behavioral changes. For instance, a popular theoretical framework interprets human behavior as a result of a conflict between cognition and emotion, with the cognitive system promoting self-interested choices, and the emotional system (triggered by the social context) operating against them. Other theories favor social norms and deontic heuristics in biasing human reasoning and encouraging choices that are sometimes in conflict with one's interest. Few studies attempted to disentangle between these (as well as other) models. As a consequence, although insightful results arise from specific domains/tasks, a comprehensive theoretical framework is still missing. Furthermore, studies employing neuroimaging techniques have begun to shed some light on the neural substrates involved in social behavior, implicating consistently (although not exclusively) portions of the limbic system, the insular and the prefrontal cortex. In this context, a challenge for present research lies not only in further mapping the brain structures implicated in social behavior, or in describing in detail the functional interaction between these structures, but in showing how the implicated networks relate to different theoretical models. This is Research Topic hosted by members of the Swiss National Center of Competence in Research "Affective Sciences - Emotions in Individual Behaviour and Social Processes". We collected contributions from the international community which extended the current knowledge about the psychological and neural structures underlying social behavior and decision making. In particular, we encouraged submissions from investigators arising from different domains (psychology, behavioral economics, affective sciences, etc.) implementing different techniques (behavior, electrophysiology, neuroimaging, brain stimulations) on different populations (neurotypical adults, children, brain damaged or psychiatric patients, etc.). Animal studies are also included, as the data reported are of high comparative value. Finally, we also welcomed submissions of meta-analytical articles, mini-reviews and perspective papers which offer provocative and insightful interpretations of the recent literature in the field. 606 $aNeurosciences$2bicssc 610 $aautism spectrum disorders(ASD) 610 $aContextual appraisal 610 $aDecision Making 610 $aEmotions 610 $aMedial prefrontal cortex 610 $aoxytocin receptor gene 610 $aSocial Behavior 610 $aultimatum game 615 7$aNeurosciences 700 $aSusanne Leiberg$4auth$01279545 702 $aPatrik Vuilleumier$4auth 702 $aLeonie Koban$4auth 702 $aCorrado Corradi-Dell'Acqua$4auth 702 $aErnst Fehr$4auth 906 $aBOOK 912 $a9910220034403321 996 $aWhat Determines Social Behavior? Investigating the Role of Emotions, Self-Centered Motives, and Social Norms$93015579 997 $aUNINA