Matrix Partial Orders, Shorted Operators and Applications
Matrix Partial Orders, Shorted Operators and Applications

Author: Sujit Kumar Mitra

Publisher: World Scientific

Published: 2010

Total Pages: 463

ISBN-13: 9812838449

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The present monograph on matrix partial orders, appearing for the first time, is a unique presentation of many partial orders on matrices that have fascinated mathematicians for their beauty and applied scientists for their wide-ranging application potential. Except for the Lwner order, the partial orders considered are relatively new and came into being in the late 1970s. After a detailed introduction to generalized inverses and decompositions, the three basic partial orders namely, the minus, the sharp and the star and the corresponding one-sided orders are presented using various generalized inverses. The authors then give a unified theory of all these partial orders. This is followed by a study of the Lwner order and a limited treatment of majorization (there is an abundance of literature available on majorization). The authors also study the parallel sums and shorted matrices, the latter being studied at great length. Partial orders of modified matrices are a new addition. Finally, applications are given in statistics and electrical network theory.

Combinatorial Matrix Theory and Generalized Inverses of Matrices
Combinatorial Matrix Theory and Generalized Inverses of Matrices

Author: Ravindra B. Bapat

Publisher: Springer Science & Business Media

Published: 2013-02-11

Total Pages: 283

ISBN-13: 8132210530

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This book consists of eighteen articles in the area of `Combinatorial Matrix Theory' and `Generalized Inverses of Matrices'. Original research and expository articles presented in this publication are written by leading Mathematicians and Statisticians working in these areas. The articles contained herein are on the following general topics: `matrices in graph theory', `generalized inverses of matrices', `matrix methods in statistics' and `magic squares'. In the area of matrices and graphs, speci_c topics addressed in this volume include energy of graphs, q-analog, immanants of matrices and graph realization of product of adjacency matrices. Topics in the book from `Matrix Methods in Statistics' are, for example, the analysis of BLUE via eigenvalues of covariance matrix, copulas, error orthogonal model, and orthogonal projectors in the linear regression models. Moore-Penrose inverse of perturbed operators, reverse order law in the case of inde_nite inner product space, approximation numbers, condition numbers, idempotent matrices, semiring of nonnegative matrices, regular matrices over incline and partial order of matrices are the topics addressed under the area of theory of generalized inverses. In addition to the above traditional topics and a report on CMTGIM 2012 as an appendix, we have an article on old magic squares from India.

Matrix Tricks for Linear Statistical Models
Matrix Tricks for Linear Statistical Models

Author: Simo Puntanen

Publisher: Springer Science & Business Media

Published: 2011-08-24

Total Pages: 504

ISBN-13: 3642104738

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In teaching linear statistical models to first-year graduate students or to final-year undergraduate students there is no way to proceed smoothly without matrices and related concepts of linear algebra; their use is really essential. Our experience is that making some particular matrix tricks very familiar to students can substantially increase their insight into linear statistical models (and also multivariate statistical analysis). In matrix algebra, there are handy, sometimes even very simple “tricks” which simplify and clarify the treatment of a problem—both for the student and for the professor. Of course, the concept of a trick is not uniquely defined—by a trick we simply mean here a useful important handy result. In this book we collect together our Top Twenty favourite matrix tricks for linear statistical models.

Applied Linear Algebra, Probability and Statistics
Applied Linear Algebra, Probability and Statistics

Author: Ravindra B. Bapat

Publisher: Springer Nature

Published: 2023-07-31

Total Pages: 540

ISBN-13: 9819923107

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This book focuses on research in linear algebra, statistics, matrices, graphs and their applications. Many chapters in the book feature new findings due to applications of matrix and graph methods. The book also discusses rediscoveries of the subject by using new methods. Dedicated to Prof. Calyampudi Radhakrishna Rao (C.R. Rao) who has completed 100 years of legendary life and continues to inspire us all and Prof. Arbind K. Lal who has sadly departed us too early, it has contributions from collaborators, students, colleagues and admirers of Professors Rao and Lal. With many chapters on generalized inverses, matrix analysis, matrices and graphs, applied probability and statistics, and the history of ancient mathematics, this book offers a diverse array of mathematical results, techniques and applications. The book promises to be especially rewarding for readers with an interest in the focus areas of applied linear algebra, probability and statistics.

Matrix Information Geometry
Matrix Information Geometry

Author: Frank Nielsen

Publisher: Springer Science & Business Media

Published: 2012-08-07

Total Pages: 454

ISBN-13: 3642302327

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This book presents advances in matrix and tensor data processing in the domain of signal, image and information processing. The theoretical mathematical approaches are discusses in the context of potential applications in sensor and cognitive systems engineering. The topics and application include Information Geometry, Differential Geometry of structured Matrix, Positive Definite Matrix, Covariance Matrix, Sensors (Electromagnetic Fields, Acoustic sensors) and Applications in Cognitive systems, in particular Data Mining.

Current Trends in Matrix Theory
Current Trends in Matrix Theory

Author: Frank Uhlig

Publisher: North Holland

Published: 1987

Total Pages: 480

ISBN-13:

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This volume contains 41 original papers and 22 abstracts of research in linear algebra and applications currently conducted by many of the leading experts in the field. More than a dozen of the papers are survey articles, while several propose open problems. The applications range from control to probability theory, with strong emphasis on matrix polynomials, Schur complements, permanents, numerical computation, combinatorics, and core linear algebra.

SIAM Journal on Matrix Analysis and Applications
SIAM Journal on Matrix Analysis and Applications

Author:

Publisher:

Published: 1990

Total Pages: 724

ISBN-13:

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Contains research articles on linear algebra with emphasis on applications and numerical procedures. These applications include such areas as Markov chains, networks, signal processing, systems and control theory, mathematical programming, economic and biological modeling, and statistics and operations research.