The Real Positive Definite Complection Problem

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The Real Positive Definite Completion Problem: Cycle Completability

Author : Wayne Walton Barrett
Publisher : American Mathematical Soc.
ISBN 13 : 0821804731
Total Pages : 82 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis The Real Positive Definite Completion Problem: Cycle Completability by : Wayne Walton Barrett

Download or read book The Real Positive Definite Completion Problem: Cycle Completability written by Wayne Walton Barrett and published by American Mathematical Soc.. This book was released on 1996 with total page 82 pages. Available in PDF, EPUB and Kindle. Book excerpt: Given a partial symmetric matrix, the positive definite completion problem asks if the unspecified entries in the matrix can be chosen so as to make the resulting matrix positive definite. Applications include probability and statistics, image enhancement, systems engineering, geophysics, and mathematical programming. The positive definite completion problem can also be viewed as a mechanism for addressing a fundamental problem in Euclidean geometry: which potential geometric configurations of vectors (i.e., configurations with angles between some vectors specified) are realizable in a Euclidean space. The positions of the specified entries in a partial matrix are naturally described by a graph. The question of existence of a positive definite completion was previously solved completely for the restrictive class of chordal graphs and this work solves the problem for the class of cycle completable graphs, a significant generalization of chordal graphs. These are graphs for which knowledge of completability for induced cycles (and cliques) implies completability of partial symmetric matrices with the given graph.

Completion Problems on Operator Matrices

Author : Dragana S. Cvetković Ilić
Publisher : American Mathematical Society
ISBN 13 : 1470469871
Total Pages : 170 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Completion Problems on Operator Matrices by : Dragana S. Cvetković Ilić

Download or read book Completion Problems on Operator Matrices written by Dragana S. Cvetković Ilić and published by American Mathematical Society. This book was released on 2022-06-07 with total page 170 pages. Available in PDF, EPUB and Kindle. Book excerpt: Completion problems for operator matrices are concerned with the question of whether a partially specified operator matrix can be completed to form an operator of a desired type. The research devoted to this topic provides an excellent means to investigate the structure of operators. This book provides an overview of completion problems dealing with completions to different types of operators and can be considered as a natural extension of classical results concerned with matrix completions. The book assumes some basic familiarity with functional analysis and operator theory. It will be useful for graduate students and researchers interested in operator theory and the problem of matrix completions.

Generalized Symplectic Geometries and the Index of Families of Elliptic Problems

Author : Liviu I. Nicolaescu
Publisher : American Mathematical Soc.
ISBN 13 : 0821806211
Total Pages : 98 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Generalized Symplectic Geometries and the Index of Families of Elliptic Problems by : Liviu I. Nicolaescu

Download or read book Generalized Symplectic Geometries and the Index of Families of Elliptic Problems written by Liviu I. Nicolaescu and published by American Mathematical Soc.. This book was released on 1997 with total page 98 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, an index theorem is proved for arbitrary families of elliptic boundary value problems for Dirac operators and a surgery formula for the index of a family of Dirac operators on a closed manifold. Also obtained is a very general result on the cobordism invariance of the index of a family. All results are established by first symplectically rephrasing the problems and then using a generalized symplectic reduction technique. This provides a unified approach to all possible parameter spaces and all possible symmetries of a Dirac operator (eigh symmetries in the real case and two in the complex case). This text will also be of interest to those working in geometry and topology.

Decision Problems for Equational Theories of Relation Algebras

Author : H. Andréka
Publisher : American Mathematical Soc.
ISBN 13 : 0821805959
Total Pages : 146 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Decision Problems for Equational Theories of Relation Algebras by : H. Andréka

Download or read book Decision Problems for Equational Theories of Relation Algebras written by H. Andréka and published by American Mathematical Soc.. This book was released on 1997 with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt: "We prove that any variety of relation algebras which contains an algebra with infinitely many elements below the identity, or which contains the full group relation algebra on some infinite group (or on arbitrarily large finite groups), must have an undecidable equational theory. Then we construct an embedding of the lattice of all subsets of the natural numbers into the lattice of varieties of relation algebras such that the variety correlated with a set [italic capital]X of natural numbers has a decidable equational theory if and only if [italic capital]X is a decidable (i.e., recursive) set. Finally, we construct an example of an infinite, finitely generated, simple, representable relation algebra that has a decidable equational theory.'' -- Abstract.

Completely Positive Matrices

Author : Abraham Berman
Publisher : World Scientific
ISBN 13 : 9814486000
Total Pages : 218 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Completely Positive Matrices by : Abraham Berman

Download or read book Completely Positive Matrices written by Abraham Berman and published by World Scientific. This book was released on 2003-04-11 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: A real matrix is positive semidefinite if it can be decomposed as A=BB′. In some applications the matrix B has to be elementwise nonnegative. If such a matrix exists, A is called completely positive. The smallest number of columns of a nonnegative matrix B such that A=BB′ is known as the cp-rank of A.This invaluable book focuses on necessary conditions and sufficient conditions for complete positivity, as well as bounds for the cp-rank. The methods are combinatorial, geometric and algebraic. The required background on nonnegative matrices, cones, graphs and Schur complements is outlined.

Handbook of Graphical Models

Author : Marloes Maathuis
Publisher : CRC Press
ISBN 13 : 0429874235
Total Pages : 612 pages
Book Rating : 4.4/5 (298 download)

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Book Synopsis Handbook of Graphical Models by : Marloes Maathuis

Download or read book Handbook of Graphical Models written by Marloes Maathuis and published by CRC Press. This book was released on 2018-11-12 with total page 612 pages. Available in PDF, EPUB and Kindle. Book excerpt: A graphical model is a statistical model that is represented by a graph. The factorization properties underlying graphical models facilitate tractable computation with multivariate distributions, making the models a valuable tool with a plethora of applications. Furthermore, directed graphical models allow intuitive causal interpretations and have become a cornerstone for causal inference. While there exist a number of excellent books on graphical models, the field has grown so much that individual authors can hardly cover its entire scope. Moreover, the field is interdisciplinary by nature. Through chapters by leading researchers from different areas, this handbook provides a broad and accessible overview of the state of the art. Key features: * Contributions by leading researchers from a range of disciplines * Structured in five parts, covering foundations, computational aspects, statistical inference, causal inference, and applications * Balanced coverage of concepts, theory, methods, examples, and applications * Chapters can be read mostly independently, while cross-references highlight connections The handbook is targeted at a wide audience, including graduate students, applied researchers, and experts in graphical models.

Families of Curves in ${\mathbb P}^3$ and Zeuthen's Problem

$Download Families of Curves in ${\mathbb P}^3$ and Zeuthen's Problem PDF Online Free$

Author : Robin Hartshorne
Publisher : American Mathematical Soc.
ISBN 13 : 0821806483
Total Pages : 111 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Families of Curves in ${\mathbb P}^3$ and Zeuthen's Problem by : Robin Hartshorne

Download or read book Families of Curves in ${\mathbb P}^3$ and Zeuthen's Problem written by Robin Hartshorne and published by American Mathematical Soc.. This book was released on 1997 with total page 111 pages. Available in PDF, EPUB and Kindle. Book excerpt: Content Description #"November 1997, volume 130, number 617 (first of 4 numbers)."#On t.p. "P" is blackboard bold.#Includes bibliographical references.

Matrix Theory and Applications

Author : Charles R. Johnson
Publisher : American Mathematical Soc.
ISBN 13 : 0821801546
Total Pages : 272 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Matrix Theory and Applications by : Charles R. Johnson

Download or read book Matrix Theory and Applications written by Charles R. Johnson and published by American Mathematical Soc.. This book was released on 1990 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the lecture notes prepared for the AMS Short Course on Matrix Theory and Applications, held in Phoenix in January, 1989. Matrix theory continues to enjoy a renaissance that has accelerated in the past decade, in part because of stimulation from a variety of applications and considerable interplay with other parts of mathematics. In addition, the great increase in the number and vitality of specialists in the field has dispelled the popular misconception that the subject has been fully researched.

Handbook of Linear Algebra

Author : Leslie Hogben
Publisher : CRC Press
ISBN 13 : 1466507292
Total Pages : 1838 pages
Book Rating : 4.4/5 (665 download)

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Book Synopsis Handbook of Linear Algebra by : Leslie Hogben

Download or read book Handbook of Linear Algebra written by Leslie Hogben and published by CRC Press. This book was released on 2013-11-26 with total page 1838 pages. Available in PDF, EPUB and Kindle. Book excerpt: With a substantial amount of new material, the Handbook of Linear Algebra, Second Edition provides comprehensive coverage of linear algebra concepts, applications, and computational software packages in an easy-to-use format. It guides you from the very elementary aspects of the subject to the frontiers of current research. Along with revisions and

Topics in Semidefinite and Interior-Point Methods

Author : Panos M. Pardalos
Publisher : American Mathematical Soc.
ISBN 13 : 0821808257
Total Pages : 272 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Topics in Semidefinite and Interior-Point Methods by : Panos M. Pardalos

Download or read book Topics in Semidefinite and Interior-Point Methods written by Panos M. Pardalos and published by American Mathematical Soc.. This book was released on 1998 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents refereed papers presented at the workshop Semidefinite Programming and Interior-Point Approaches for Combinatorial Problems: held at The Fields Institute in May 1996. Semidefinite programming (SDP) is a generalization of linear programming (LP) in that the non-negativity constraints on the variables is replaced by a positive semidefinite constraint on matrix variables. Many of the elegant theoretical properties and powerful solution techniques follow through from LP to SDP. In particular, the primal-dual interior-point methods, which are currently so successful for LP, can be used to efficiently solve SDP problems. In addition to the theoretical and algorithmic questions, SDP has found many important applications in combinatorial optimization, control theory and other areas of mathematical programming. The papers in this volume cover a wide spectrum of recent developments in SDP. The volume would be suitable as a textbook for advanced courses in optimization. It is intended for graduate students and researchers in mathematics, computer science, engineering and operations.

Algebraic Statistics

Author : Seth Sullivant
Publisher : American Mathematical Society
ISBN 13 : 1470475103
Total Pages : 506 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Algebraic Statistics by : Seth Sullivant

Download or read book Algebraic Statistics written by Seth Sullivant and published by American Mathematical Society. This book was released on 2023-11-17 with total page 506 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algebraic statistics uses tools from algebraic geometry, commutative algebra, combinatorics, and their computational sides to address problems in statistics and its applications. The starting point for this connection is the observation that many statistical models are semialgebraic sets. The algebra/statistics connection is now over twenty years old, and this book presents the first broad introductory treatment of the subject. Along with background material in probability, algebra, and statistics, this book covers a range of topics in algebraic statistics including algebraic exponential families, likelihood inference, Fisher's exact test, bounds on entries of contingency tables, design of experiments, identifiability of hidden variable models, phylogenetic models, and model selection. With numerous examples, references, and over 150 exercises, this book is suitable for both classroom use and independent study.

Encyclopedia of Optimization

Author : Christodoulos A. Floudas
Publisher : Springer Science & Business Media
ISBN 13 : 0387747583
Total Pages : 4646 pages
Book Rating : 4.3/5 (877 download)

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Book Synopsis Encyclopedia of Optimization by : Christodoulos A. Floudas

Download or read book Encyclopedia of Optimization written by Christodoulos A. Floudas and published by Springer Science & Business Media. This book was released on 2008-09-04 with total page 4646 pages. Available in PDF, EPUB and Kindle. Book excerpt: The goal of the Encyclopedia of Optimization is to introduce the reader to a complete set of topics that show the spectrum of research, the richness of ideas, and the breadth of applications that has come from this field. The second edition builds on the success of the former edition with more than 150 completely new entries, designed to ensure that the reference addresses recent areas where optimization theories and techniques have advanced. Particularly heavy attention resulted in health science and transportation, with entries such as "Algorithms for Genomics", "Optimization and Radiotherapy Treatment Design", and "Crew Scheduling".

Convex Optimization

Author : Stephen P. Boyd
Publisher : Cambridge University Press
ISBN 13 : 9780521833783
Total Pages : 744 pages
Book Rating : 4.8/5 (337 download)

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Book Synopsis Convex Optimization by : Stephen P. Boyd

Download or read book Convex Optimization written by Stephen P. Boyd and published by Cambridge University Press. This book was released on 2004-03-08 with total page 744 pages. Available in PDF, EPUB and Kindle. Book excerpt: Convex optimization problems arise frequently in many different fields. This book provides a comprehensive introduction to the subject, and shows in detail how such problems can be solved numerically with great efficiency. The book begins with the basic elements of convex sets and functions, and then describes various classes of convex optimization problems. Duality and approximation techniques are then covered, as are statistical estimation techniques. Various geometrical problems are then presented, and there is detailed discussion of unconstrained and constrained minimization problems, and interior-point methods. The focus of the book is on recognizing convex optimization problems and then finding the most appropriate technique for solving them. It contains many worked examples and homework exercises and will appeal to students, researchers and practitioners in fields such as engineering, computer science, mathematics, statistics, finance and economics.

Issues in Logic, Probability, Combinatorics, and Chaos Theory: 2013 Edition

Author :
Publisher : ScholarlyEditions
ISBN 13 : 1490107509
Total Pages : 1039 pages
Book Rating : 4.4/5 (91 download)

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Book Synopsis Issues in Logic, Probability, Combinatorics, and Chaos Theory: 2013 Edition by :

Download or read book Issues in Logic, Probability, Combinatorics, and Chaos Theory: 2013 Edition written by and published by ScholarlyEditions. This book was released on 2013-05-01 with total page 1039 pages. Available in PDF, EPUB and Kindle. Book excerpt: Issues in Logic, Probability, Combinatorics, and Chaos Theory: 2013 Edition is a ScholarlyEditions™ book that delivers timely, authoritative, and comprehensive information about Approximation Theory. The editors have built Issues in Logic, Probability, Combinatorics, and Chaos Theory: 2013 Edition on the vast information databases of ScholarlyNews.™ You can expect the information about Approximation Theory in this book to be deeper than what you can access anywhere else, as well as consistently reliable, authoritative, informed, and relevant. The content of Issues in Logic, Probability, Combinatorics, and Chaos Theory: 2013 Edition has been produced by the world’s leading scientists, engineers, analysts, research institutions, and companies. All of the content is from peer-reviewed sources, and all of it is written, assembled, and edited by the editors at ScholarlyEditions™ and available exclusively from us. You now have a source you can cite with authority, confidence, and credibility. More information is available at http://www.ScholarlyEditions.com/.

Matrix Completions, Moments, and Sums of Hermitian Squares

Author : Mihály Bakonyi
Publisher : Princeton University Press
ISBN 13 : 1400840597
Total Pages : 533 pages
Book Rating : 4.4/5 (8 download)

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Book Synopsis Matrix Completions, Moments, and Sums of Hermitian Squares by : Mihály Bakonyi

Download or read book Matrix Completions, Moments, and Sums of Hermitian Squares written by Mihály Bakonyi and published by Princeton University Press. This book was released on 2011-07-18 with total page 533 pages. Available in PDF, EPUB and Kindle. Book excerpt: Intensive research in matrix completions, moments, and sums of Hermitian squares has yielded a multitude of results in recent decades. This book provides a comprehensive account of this quickly developing area of mathematics and applications and gives complete proofs of many recently solved problems. With MATLAB codes and more than 200 exercises, the book is ideal for a special topics course for graduate or advanced undergraduate students in mathematics or engineering, and will also be a valuable resource for researchers. Often driven by questions from signal processing, control theory, and quantum information, the subject of this book has inspired mathematicians from many subdisciplines, including linear algebra, operator theory, measure theory, and complex function theory. In turn, the applications are being pursued by researchers in areas such as electrical engineering, computer science, and physics. The book is self-contained, has many examples, and for the most part requires only a basic background in undergraduate mathematics, primarily linear algebra and some complex analysis. The book also includes an extensive discussion of the literature, with close to 600 references from books and journals from a wide variety of disciplines.

Graphs and Matrices

Author : Ravindra B. Bapat
Publisher : Springer
ISBN 13 : 1447165691
Total Pages : 197 pages
Book Rating : 4.4/5 (471 download)

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Book Synopsis Graphs and Matrices by : Ravindra B. Bapat

Download or read book Graphs and Matrices written by Ravindra B. Bapat and published by Springer. This book was released on 2014-09-19 with total page 197 pages. Available in PDF, EPUB and Kindle. Book excerpt: This new edition illustrates the power of linear algebra in the study of graphs. The emphasis on matrix techniques is greater than in other texts on algebraic graph theory. Important matrices associated with graphs (for example, incidence, adjacency and Laplacian matrices) are treated in detail. Presenting a useful overview of selected topics in algebraic graph theory, early chapters of the text focus on regular graphs, algebraic connectivity, the distance matrix of a tree, and its generalized version for arbitrary graphs, known as the resistance matrix. Coverage of later topics include Laplacian eigenvalues of threshold graphs, the positive definite completion problem and matrix games based on a graph. Such an extensive coverage of the subject area provides a welcome prompt for further exploration. The inclusion of exercises enables practical learning throughout the book. In the new edition, a new chapter is added on the line graph of a tree, while some results in Chapter 6 on Perron-Frobenius theory are reorganized. Whilst this book will be invaluable to students and researchers in graph theory and combinatorial matrix theory, it will also benefit readers in the sciences and engineering.

Positive Definite Matrices

Author : Rajendra Bhatia
Publisher : Princeton University Press
ISBN 13 : 1400827787
Total Pages : 265 pages
Book Rating : 4.4/5 (8 download)

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Book Synopsis Positive Definite Matrices by : Rajendra Bhatia

Download or read book Positive Definite Matrices written by Rajendra Bhatia and published by Princeton University Press. This book was released on 2009-01-10 with total page 265 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book represents the first synthesis of the considerable body of new research into positive definite matrices. These matrices play the same role in noncommutative analysis as positive real numbers do in classical analysis. They have theoretical and computational uses across a broad spectrum of disciplines, including calculus, electrical engineering, statistics, physics, numerical analysis, quantum information theory, and geometry. Through detailed explanations and an authoritative and inspiring writing style, Rajendra Bhatia carefully develops general techniques that have wide applications in the study of such matrices. Bhatia introduces several key topics in functional analysis, operator theory, harmonic analysis, and differential geometry--all built around the central theme of positive definite matrices. He discusses positive and completely positive linear maps, and presents major theorems with simple and direct proofs. He examines matrix means and their applications, and shows how to use positive definite functions to derive operator inequalities that he and others proved in recent years. He guides the reader through the differential geometry of the manifold of positive definite matrices, and explains recent work on the geometric mean of several matrices. Positive Definite Matrices is an informative and useful reference book for mathematicians and other researchers and practitioners. The numerous exercises and notes at the end of each chapter also make it the ideal textbook for graduate-level courses.