Statistical Applications of Jordan Algebras

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Publisher : Springer Science & Business Media
ISBN 13 : 1461226783
Total Pages : 110 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Statistical Applications of Jordan Algebras by : James D. Malley

Download or read book Statistical Applications of Jordan Algebras written by James D. Malley and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 110 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph brings together my work in mathematical statistics as I have viewed it through the lens of Jordan algebras. Three technical domains are to be seen: applications to random quadratic forms (sums of squares), the investigation of algebraic simplifications of maxi mum likelihood estimation of patterned covariance matrices, and a more wide open mathematical exploration of the algebraic arena from which I have drawn the results used in the statistical problems just mentioned. Chapters 1, 2, and 4 present the statistical outcomes I have developed using the algebraic results that appear, for the most part, in Chapter 3. As a less daunting, yet quite efficient, point of entry into this material, one avoiding most of the abstract algebraic issues, the reader may use the first half of Chapter 4. Here I present a streamlined, but still fully rigorous, definition of a Jordan algebra (as it is used in that chapter) and its essential properties. These facts are then immediately applied to simplifying the M:-step of the EM algorithm for multivariate normal covariance matrix estimation, in the presence of linear constraints, and data missing completely at random. The results presented essentially resolve a practical statistical quest begun by Rubin and Szatrowski [1982], and continued, sometimes implicitly, by many others. After this, one could then return to Chapters 1 and 2 to see how I have attempted to generalize the work of Cochran, Rao, Mitra, and others, on important and useful properties of sums of squares.

The Minnesota Notes on Jordan Algebras and Their Applications

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Publisher : Springer
ISBN 13 : 3540484027
Total Pages : 180 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis The Minnesota Notes on Jordan Algebras and Their Applications by : Max Koecher

Download or read book The Minnesota Notes on Jordan Algebras and Their Applications written by Max Koecher and published by Springer. This book was released on 2006-11-14 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains a re-edition of Max Koecher's famous Minnesota Notes. The main objects are homogeneous, but not necessarily convex, cones. They are described in terms of Jordan algebras. The central point is a correspondence between semisimple real Jordan algebras and so-called omega-domains. This leads to a construction of half-spaces which give an essential part of all bounded symmetric domains. The theory is presented in a concise manner, with only elementary prerequisites. The editors have added notes on each chapter containing an account of the relevant developments of the theory since these notes were first written.

The Minnesota Notes on Jordan Algebras and Their Applications

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Publisher :
ISBN 13 : 9783662162750
Total Pages : 198 pages
Book Rating : 4.1/5 (627 download)

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Book Synopsis The Minnesota Notes on Jordan Algebras and Their Applications by : Max Krieg Aloys Koecher

Download or read book The Minnesota Notes on Jordan Algebras and Their Applications written by Max Krieg Aloys Koecher and published by . This book was released on 2014-01-15 with total page 198 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Jordan Algebras and Their Applications

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Publisher :
ISBN 13 :
Total Pages : 316 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Jordan Algebras and Their Applications by : Max Koecher

Download or read book Jordan Algebras and Their Applications written by Max Koecher and published by . This book was released on 1962 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Jordan Algebras in Analysis, Operator Theory, and Quantum Mechanics

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Publisher : American Mathematical Soc.
ISBN 13 : 082180717X
Total Pages : 95 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Jordan Algebras in Analysis, Operator Theory, and Quantum Mechanics by : Harald Upmeier

Download or read book Jordan Algebras in Analysis, Operator Theory, and Quantum Mechanics written by Harald Upmeier and published by American Mathematical Soc.. This book was released on 1987 with total page 95 pages. Available in PDF, EPUB and Kindle. Book excerpt: Jordan algebras have found interesting applications in seemingly unrelated areas of mathematics such as operator theory, the foundations of quantum mechanics, complex analysis in finite and infinite dimensions, and harmonic analysis on homogeneous spaces. This book describes some relevant results and puts them in a general framework.

Structure and Representations of Jordan Algebras

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Publisher : American Mathematical Soc.
ISBN 13 : 082184640X
Total Pages : 464 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Structure and Representations of Jordan Algebras by : Nathan Jacobson

Download or read book Structure and Representations of Jordan Algebras written by Nathan Jacobson and published by American Mathematical Soc.. This book was released on 1968-12-31 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of Jordan algebras has played important roles behind the scenes of several areas of mathematics. Jacobson's book has long been the definitive treatment of the subject. It covers foundational material, structure theory, and representation theory for Jordan algebras. Of course, there are immediate connections with Lie algebras, which Jacobson details in Chapter 8. Of particular continuing interest is the discussion of exceptional Jordan algebras, which serve to explain the exceptional Lie algebras and Lie groups. Jordan algebras originally arose in the attempts by Jordan, von Neumann, and Wigner to formulate the foundations of quantum mechanics. They are still useful and important in modern mathematical physics, as well as in Lie theory, geometry, and certain areas of analysis.

A Taste of Jordan Algebras

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Publisher : Springer Science & Business Media
ISBN 13 : 0387217967
Total Pages : 584 pages
Book Rating : 4.3/5 (872 download)

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Book Synopsis A Taste of Jordan Algebras by : Kevin McCrimmon

Download or read book A Taste of Jordan Algebras written by Kevin McCrimmon and published by Springer Science & Business Media. This book was released on 2006-05-29 with total page 584 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes the history of Jordan algebras and describes in full mathematical detail the recent structure theory for Jordan algebras of arbitrary dimension due to Efim Zel'manov. Jordan algebras crop up in many surprising settings, and find application to a variety of mathematical areas. No knowledge is required beyond standard first-year graduate algebra courses.

Banach Algebras and Their Applications

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Publisher : American Mathematical Soc.
ISBN 13 : 0821834711
Total Pages : 362 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Banach Algebras and Their Applications by : Anthony To-Ming Lau

Download or read book Banach Algebras and Their Applications written by Anthony To-Ming Lau and published by American Mathematical Soc.. This book was released on 2004 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: This proceedings volume is from the international conference on Banach Algebras and Their Applications held at the University of Alberta (Edmonton). It contains a collection of refereed research papers and high-level expository articles that offer a panorama of Banach algebra theory and its manifold applications. Topics in the book range from - theory to abstract harmonic analysis to operator theory. It is suitable for graduate students and researchers interested in Banach algebras.

Topological Algebras and their Applications

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Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110413558
Total Pages : 318 pages
Book Rating : 4.1/5 (14 download)

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Book Synopsis Topological Algebras and their Applications by : Alexander Katz

Download or read book Topological Algebras and their Applications written by Alexander Katz and published by Walter de Gruyter GmbH & Co KG. This book was released on 2018-05-07 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proceedings of the 8th International Conference of Topological Algebras and Their Applications (ICTAA-2014), held on May 26-30, 2014 in Playa de Villas de Mar Beach, dedicated to the memory of Anastasios Mallios (Athens, Greece). This series of conferences started in 1999 in Tartu, Estonia and were subsequently held in Rabat, Moroco (2000), Oulu, Finland (2001), Oaxaca, Mexico (2002), Bedlewo, Poland (2003), Athens, Greece (2005) and Tartu, Estonia (2008 and 2013). The topics of the conference include all areas of mathematics, connected with (preferably general) topological algebras and their applications, including all kinds of topological-algebraic structures as topological linear spaces, topological rings, topological modules, topological groups and semigroups; bornological-algebraic structures such as bornological linear spaces, bornological algebras, bornological groups, bornological rings and modules; algebraic and topological K-theory; topological module bundles, sheaves and others. Contents Some results on spectral properties of unital algebras and on the algebra of linear operators on a unital algebra Descriptions of all closed maximal one-sided ideals in topological algebras On non self-adjoint operators defined by Riesz bases in Hilbert and rigged Hilbert spaces Functional calculus on algebras of operators generated by a self-adjoint operator in Pontryagin space Π1 On Gelfand-Naimark type Theorems for unital abelian complex and real locally C*-, and locally JB-algebras Multipliers and strictly real topological algebras Multipliers in some perfect locally m-pseudo-convex algebras Wedderburn structure theorems for two-sided locally m-convex H*-algebras Homologically best modules in classical and quantized functional analysis Operator Grüss inequality Main embedding theorems for symmetric spaces of measurable functions Mapping class groups are linear Subnormable A-convex algebras Commutative BP*-algebras and Gelfand-Naimark’s theorem Discrete nonclosed subsets in maximally nondiscrete topological groups Faithfully representable topological *-algebras: some spectral properties On continuity of complementors in topological algebras Dominated ergodic theorem for isometries of non-commutative Lp-spaces, 1 p p ≠ 2 Ranks and the approximate n-th root property of C*-algebras Dense ideals in topological algebras: some results and open problems

Jordan Structures in Lie Algebras

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Publisher : American Mathematical Soc.
ISBN 13 : 1470450860
Total Pages : 314 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Jordan Structures in Lie Algebras by : Antonio Fernández López

Download or read book Jordan Structures in Lie Algebras written by Antonio Fernández López and published by American Mathematical Soc.. This book was released on 2019-08-19 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: Explores applications of Jordan theory to the theory of Lie algebras. After presenting the general theory of nonassociative algebras and of Lie algebras, the book then explains how properties of the Jordan algebra attached to a Jordan element of a Lie algebra can be used to reveal properties of the Lie algebra itself.

Jordan algebras with applications

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Publisher :
ISBN 13 :
Total Pages : 170 pages
Book Rating : 4.:/5 (633 download)

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Book Synopsis Jordan algebras with applications by : Radu Iordanescu

Download or read book Jordan algebras with applications written by Radu Iordanescu and published by . This book was released on 1979 with total page 170 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Algebra and Applications 1

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Publisher : John Wiley & Sons
ISBN 13 : 1119818168
Total Pages : 368 pages
Book Rating : 4.1/5 (198 download)

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Book Synopsis Algebra and Applications 1 by : Abdenacer Makhlouf

Download or read book Algebra and Applications 1 written by Abdenacer Makhlouf and published by John Wiley & Sons. This book was released on 2021-03-12 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is part of Algebra and Geometry, a subject within the SCIENCES collection published by ISTE and Wiley, and the first of three volumes specifically focusing on algebra and its applications. Algebra and Applications 1 centers on non-associative algebras and includes an introduction to derived categories. The chapters are written by recognized experts in the field, providing insight into new trends, as well as a comprehensive introduction to the theory. The book incorporates self-contained surveys with the main results, applications and perspectives. The chapters in this volume cover a wide variety of algebraic structures and their related topics. Jordan superalgebras, Lie algebras, composition algebras, graded division algebras, non-associative C*- algebras, H*-algebras, Krichever-Novikov type algebras, preLie algebras and related structures, geometric structures on 3-Lie algebras and derived categories are all explored. Algebra and Applications 1 is of great interest to graduate students and researchers. Each chapter combines some of the features of both a graduate level textbook and of research level surveys.

Geometry of State Spaces of Operator Algebras

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Publisher : Springer Science & Business Media
ISBN 13 : 1461200199
Total Pages : 470 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Geometry of State Spaces of Operator Algebras by : Erik M. Alfsen

Download or read book Geometry of State Spaces of Operator Algebras written by Erik M. Alfsen and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 470 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book we give a complete geometric description of state spaces of operator algebras, Jordan as well as associative. That is, we give axiomatic characterizations of those convex sets that are state spaces of C*-algebras and von Neumann algebras, together with such characterizations for the normed Jordan algebras called JB-algebras and JBW-algebras. These non associative algebras generalize C*-algebras and von Neumann algebras re spectively, and the characterization of their state spaces is not only of interest in itself, but is also an important intermediate step towards the characterization of the state spaces of the associative algebras. This book gives a complete and updated presentation of the character ization theorems of [10]' [11] and [71]. Our previous book State spaces of operator algebras: basic theory, orientations and C*-products, referenced as [AS] in the sequel, gives an account of the necessary prerequisites on C*-algebras and von Neumann algebras, as well as a discussion of the key notion of orientations of state spaces. For the convenience of the reader, we have summarized these prerequisites in an appendix which contains all relevant definitions and results (listed as (AI), (A2), ... ), with reference back to [AS] for proofs, so that this book is self-contained.

Jordan, Real and Lie Structures in Operator Algebras

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Publisher : Springer Science & Business Media
ISBN 13 : 9401586055
Total Pages : 239 pages
Book Rating : 4.4/5 (15 download)

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Book Synopsis Jordan, Real and Lie Structures in Operator Algebras by : Sh. Ayupov

Download or read book Jordan, Real and Lie Structures in Operator Algebras written by Sh. Ayupov and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 239 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of operator algebras acting on a Hilbert space was initiated in thirties by papers of Murray and von Neumann. In these papers they have studied the structure of algebras which later were called von Neu mann algebras or W* -algebras. They are weakly closed complex *-algebras of operators on a Hilbert space. At present the theory of von Neumann algebras is a deeply developed theory with various applications. In the framework of von Neumann algebras theory the study of fac tors (i.e. W* -algebras with trivial centres) is very important, since they are comparatively simple and investigation of general W* -algebras can be reduced to the case of factors. Therefore the theory of factors is one of the main tools in the structure theory of von Neumann algebras. In the middle of sixtieth Topping [To 1] and Stormer [S 2] have ini tiated the study of Jordan (non associative and real) analogues of von Neumann algebras - so called JW-algebras, i.e. real linear spaces of self adjoint opera.tors on a complex Hilbert space, which contain the identity operator 1. closed with respect to the Jordan (i.e. symmetrised) product INTRODUCTION 2 x 0 y = ~(Xy + yx) and closed in the weak operator topology. The structure of these algebras has happened to be close to the struc ture of von Neumann algebras and it was possible to apply ideas and meth ods similar to von Neumann algebras theory in the study of JW-algebras.

Applications of Jordan Algebras to the Normal Subgroup Structure of SL2(R)

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Publisher :
ISBN 13 :
Total Pages : 182 pages
Book Rating : 4.X/5 (4 download)

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Book Synopsis Applications of Jordan Algebras to the Normal Subgroup Structure of SL2(R) by : Daniel John Borzynski

Download or read book Applications of Jordan Algebras to the Normal Subgroup Structure of SL2(R) written by Daniel John Borzynski and published by . This book was released on 1997 with total page 182 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Jordan Algebras

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Author :
Publisher : Walter de Gruyter
ISBN 13 : 3110878119
Total Pages : 353 pages
Book Rating : 4.1/5 (18 download)

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Book Synopsis Jordan Algebras by : Wilhelm Kaup

Download or read book Jordan Algebras written by Wilhelm Kaup and published by Walter de Gruyter. This book was released on 2011-05-02 with total page 353 pages. Available in PDF, EPUB and Kindle. Book excerpt: The series is aimed specifically at publishing peer reviewed reviews and contributions presented at workshops and conferences. Each volume is associated with a particular conference, symposium or workshop. These events cover various topics within pure and applied mathematics and provide up-to-date coverage of new developments, methods and applications.

On the Role of Division, Jordan and Related Algebras in Particle Physics

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Publisher : World Scientific
ISBN 13 : 9789810228637
Total Pages : 492 pages
Book Rating : 4.2/5 (286 download)

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Book Synopsis On the Role of Division, Jordan and Related Algebras in Particle Physics by : Feza Grsey

Download or read book On the Role of Division, Jordan and Related Algebras in Particle Physics written by Feza Grsey and published by World Scientific. This book was released on 1996 with total page 492 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph surveys the role of some associative and non-associative algebras, remarkable by their ubiquitous appearance in contemporary theoretical physics, particularly in particle physics. It concerns the interplay between division algebras, specifically quaternions and octonions, between Jordan and related algebras on the one hand, and unified theories of the basic interactions on the other. Selected applications of these algebraic structures are discussed: quaternion analyticity of Yang-Mills instantons, octonionic aspects of exceptional broken gauge, supergravity theories, division algebras in anyonic phenomena and in theories of extended objects in critical dimensions. The topics presented deal primarily with original contributions by the authors.