The Schur Complement And Its Applications

This book describes the Schur complement as a rich and basic tool in mathematical research and applications and discusses many significant results that illustrate its power and fertility. Coverage includes historical development, basic properties, eigenvalue and singular value inequalities, matrix inequalities in both finite and infinite dimensional settings, closure properties, and applications in statistics, probability, and numerical analysis.

This volume concisely presents fundamental ideas, results, and techniques in linear algebra and mainly matrix theory. Each chapter focuses on the results, techniques, and methods that are beautiful, interesting, and representative, followed by carefully selected problems. For many theorems several different proofs are given. The only prerequisites are a decent background in elementary linear algebra and calculus.

Contributed by world renowned researchers, the book features a wide range of important topics in modern statistical theory and methodology, economics and finance, ecology, education, health and sports studies, and computer and IT-data mining. It is accessible to students and of interest to experts.Many of the contributions are concerned with theoretical innovations, but all have applications in view, and some contain illustrations of the applied methods or photos of historic mathematicians.A few of the notable contributors are Ejaz Ahmed (Windsor), Joe Gani (ANU), Roger Gay (Monash), Atsuhiro Hayashi (NCUEE, Tokyo), Markus Hegland (ANU), Chris Heyde (ANU/Columbia), Jeff Hunter (Massey), Phil Lewis (Canberra), Heinz Neudecker (Amsterdam), Graham Pollard (Canberra), Simo Puntanen (Tampere), George Styan (McGill), and Goetz Trenkler (Dortmund).

This volume consists of contributions by speakers at a Conference on Algebra and its Applications that took place in Athens, Ohio, in March of 2005. It provides a snapshot of the diversity of themes and applications that interest algebraists today. The papers in this volume include some of the latest results in the theory of modules, noncommutative rings, representation theory, matrix theory, linear algebra over noncommutative rings, cryptography, error-correcting codes over finite rings, and projective-geometry codes, as well as expository articles that will provide algebraists and other mathematicians, including graduate students, with an accessible introduction to areas outside their own expertise. The book will serve both the specialist looking for the latest result and the novice seeking an accessible reference for some of the ideas and results presented here.

As an introduction to fundamental geometric concepts and tools needed for solving problems of a geometric nature using a computer, this book fills the gap between standard geometry books, which are primarily theoretical, and applied books on computer graphics, computer vision, or robotics that do not cover the underlying geometric concepts in detail. Gallier offers an introduction to affine, projective, computational, and Euclidean geometry, basics of differential geometry and Lie groups, and explores many of the practical applications of geometry. Some of these include computer vision, efficient communication, error correcting codes, cryptography, motion interpolation, and robot kinematics. This comprehensive text covers most of the geometric background needed for conducting research in computer graphics, geometric modeling, computer vision, and robotics and as such will be of interest to a wide audience including computer scientists, mathematicians, and engineers.

These multiple volumes (LNCS volumes 6016, 6017, 6018 and 6019) consist of the peer-reviewed papers from the 2010 International Conference on Compu- tional Science and Its Applications (ICCSA2010)held in Fukuoka, Japanduring March23–26,2010.ICCSA2010wasasuccessfuleventintheInternationalC- ferences on Computational Science and Its Applications (ICCSA) conference - ries, previouslyheld in Suwon, South Korea (2009), Perugia, Italy (2008), Kuala Lumpur, Malaysia (2007), Glasgow, UK (2006), Singapore (2005), Assisi, Italy (2004), Montreal, Canada (2003), and (as ICCS) Amsterdam, The Netherlands (2002) and San Francisco, USA (2001). Computational science is a main pillar of most of the present research, - dustrial and commercial activities and plays a unique role in exploiting ICT - novative technologies. The ICCSA conference series has been providing a venue to researchers and industry practitioners to discuss new ideas, to share complex problems and their solutions, and to shape new trends in computational science. ICCSA 2010 was celebrated at the host university, Kyushu Sangyo Univ- sity, Fukuoka, Japan, as part of the university’s 50th anniversary.We would like to thank Kyushu Sangyo University for hosting ICCSA this year, and for - cluding this international event in their celebrations. Also for the ?rst time this year, ICCSA organized poster sessions that present on-going projects on various aspects of computational sciences.

A comprehensive, must-have handbook of matrix methods with a unique emphasis on statistical applications This timely book, A Matrix Handbook for Statisticians, provides a comprehensive, encyclopedic treatment of matrices as they relate to both statistical concepts and methodologies. Written by an experienced authority on matrices and statistical theory, this handbook is organized by topic rather than mathematical developments and includes numerous references to both the theory behind the methods and the applications of the methods. A uniform approach is applied to each chapter, which contains four parts: a definition followed by a list of results; a short list of references to related topics in the book; one or more references to proofs; and references to applications. The use of extensive cross-referencing to topics within the book and external referencing to proofs allows for definitions to be located easily as well as interrelationships among subject areas to be recognized. A Matrix Handbook for Statisticians addresses the need for matrix theory topics to be presented together in one book and features a collection of topics not found elsewhere under one cover. These topics include: Complex matrices A wide range of special matrices and their properties Special products and operators, such as the Kronecker product Partitioned and patterned matrices Matrix analysis and approximation Matrix optimization Majorization Random vectors and matrices Inequalities, such as probabilistic inequalities Additional topics, such as rank, eigenvalues, determinants, norms, generalized inverses, linear and quadratic equations, differentiation, and Jacobians, are also included. The book assumes a fundamental knowledge of vectors and matrices, maintains a reasonable level of abstraction when appropriate, and provides a comprehensive compendium of linear algebra results with use or potential use in statistics. A Matrix Handbook for Statisticians is an essential, one-of-a-kind book for graduate-level courses in advanced statistical studies including linear and nonlinear models, multivariate analysis, and statistical computing. It also serves as an excellent self-study guide for statistical researchers.

This volume features selected, refereed papers on various aspects of statistics, matrix theory and its applications to statistics, as well as related numerical linear algebra topics and numerical solution methods, which are relevant for problems arising in statistics and in big data. The contributions were originally presented at the 25th International Workshop on Matrices and Statistics (IWMS 2016), held in Funchal (Madeira), Portugal on June 6-9, 2016. The IWMS workshop series brings together statisticians, computer scientists, data scientists and mathematicians, helping them better understand each other’s tools, and fostering new collaborations at the interface of matrix theory and statistics.