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**Author : **
**Publisher : **Springer Science & Business Media
**Release Date : **2014-02-06
**Category: ** Mathematics
**Pages : **332
**ISBN Code: ** 3319041509
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**Summary:** Matrices can be studied in different ways. They are a linear algebraic structure and have a topological/analytical aspect (for example, the normed space of matrices) and they also carry an order structure that is induced by positive semidefinite matrices. The interplay of these closely related structures is an essential feature of matrix analysis. This book explains these aspects of matrix analysis from a functional analysis point of view. After an introduction to matrices and functional analysis, it covers more advanced topics such as matrix monotone functions, matrix means, majorization and entropies. Several applications to quantum information are also included. Introduction to Matrix Analysis and Applications is appropriate for an advanced graduate course on matrix analysis, particularly aimed at studying quantum information. It can also be used as a reference for researchers in quantum information, statistics, engineering and economics.

**Author : ** Rajendra Bhatia
**Publisher : **Springer Science & Business Media
**Release Date : **2013-12-01
**Category: ** Mathematics
**Pages : **349
**ISBN Code: ** 1461206537
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**Summary:** This book presents a substantial part of matrix analysis that is functional analytic in spirit. Topics covered include the theory of majorization, variational principles for eigenvalues, operator monotone and convex functions, and perturbation of matrix functions and matrix inequalities. The book offers several powerful methods and techniques of wide applicability, and it discusses connections with other areas of mathematics.

**Author : ** Terence Tao
**Publisher : **American Mathematical Soc.
**Release Date : **2012-03-21
**Category: ** Mathematics
**Pages : **282
**ISBN Code: ** 0821874306
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**Summary:** The field of random matrix theory has seen an explosion of activity in recent years, with connections to many areas of mathematics and physics. However, this makes the current state of the field almost too large to survey in a single book. In this graduate text, we focus on one specific sector of the field, namely the spectral distribution of random Wigner matrix ensembles (such as the Gaussian Unitary Ensemble), as well as iid matrix ensembles. The text is largely self-contained and starts with a review of relevant aspects of probability theory and linear algebra. With over 200 exercises, the book is suitable as an introductory text for beginning graduate students seeking to enter the field.

**Author : ** Ilse C. F. Ipsen
**Publisher : **SIAM
**Release Date : **2009
**Category: ** Algebra
**Pages : **128
**ISBN Code: ** 089871768X
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**Summary:** The purpose of this book is to promote understanding of two phenomena: sensitivity of linear systems and least squares problems, and numerical stability of algorithms. Sensitivity and stability are analyzed as mathematical properties, without reference to finite precision arithmetic. The material is presented at a basic level, emphasizing ideas and intuition, but in a mathematically rigorous fashion. The derivations are simple and elegant, and the results are easy to understand and interpret. The book is self-contained. It was written for students in all areas of mathematics, engineering, and the computational sciences, but can easily be used for self-study. This text differs from other numerical linear algebra texts by offering the following: a systematic development of numerical conditioning; a simplified concept of numerical stability in exact arithmetic; simple derivations; a high-level view of algorithms; and results for complex matrices.

**Author : ** Carl D. Meyer
**Publisher : **SIAM
**Release Date : **2000
**Category: ** Mathematics
**Pages : **718
**ISBN Code: ** 0898719518
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**Summary:** Matrix Analysis and Applied Linear Algebra is an honest math text that circumvents the traditional definition-theorem-proof format that has bored students in the past. Meyer uses a fresh approach to introduce a variety of problems and examples ranging from the elementary to the challenging and from simple applications to discovery problems. The focus on applications is a big difference between this book and others. Meyer's book is more rigorous and goes into more depth than some. He includes some of the more contemporary topics of applied linear algebra which are not normally found in undergraduate textbooks. Modern concepts and notation are used to introduce the various aspects of linear equations, leading readers easily to numerical computations and applications. The theoretical developments are always accompanied with examples, which are worked out in detail. Each section ends with a large number of carefully chosen exercises from which the students can gain further insight.

**Author : ** Natália Bebiano
**Publisher : **Springer
**Release Date : **2017-03-01
**Category: ** Mathematics
**Pages : **347
**ISBN Code: ** 331949984X
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**Summary:** This volume presents recent advances in the field of matrix analysis based on contributions at the MAT-TRIAD 2015 conference. Topics covered include interval linear algebra and computational complexity, Birkhoff polynomial basis, tensors, graphs, linear pencils, K-theory and statistic inference, showing the ubiquity of matrices in different mathematical areas. With a particular focus on matrix and operator theory, statistical models and computation, the International Conference on Matrix Analysis and its Applications 2015, held in Coimbra, Portugal, was the sixth in a series of conferences. Applied and Computational Matrix Analysis will appeal to graduate students and researchers in theoretical and applied mathematics, physics and engineering who are seeking an overview of recent problems and methods in matrix analysis.

**Author : ** Sudipto Banerjee,Anindya Roy
**Publisher : **CRC Press
**Release Date : **2014-06-06
**Category: ** Mathematics
**Pages : **580
**ISBN Code: ** 1482248247
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**Summary:** Assuming no prior knowledge of linear algebra, this self-contained text offers a gradual exposition to linear algebra without sacrificing the rigor of the subject. It presents both the vector space approach and the canonical forms in matrix theory. The book covers important topics in linear algebra that are useful for statisticians, including the concept of rank, the fundamental theorem of linear algebra, projectors, and quadratic forms. It also provides an extensive collection of exercises on theoretical concepts and numerical computations.

**Author : ** Thomas Holgersson,Martin Singull
**Publisher : **Springer Nature
**Release Date : **2020-09-17
**Category: ** Mathematics
**Pages : **373
**ISBN Code: ** 3030567737
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**Summary:** This volume is a tribute to Professor Dietrich von Rosen on the occasion of his 65th birthday. It contains a collection of twenty original papers. The contents of the papers evolve around multivariate analysis and random matrices with topics such as high-dimensional analysis, goodness-of-fit measures, variable selection and information criteria, inference of covariance structures, the Wishart distribution and growth curve models.

**Author : ** Jan R. Magnus,Heinz Neudecker
**Publisher : **John Wiley & Sons
**Release Date : **2019-03-15
**Category: ** Mathematics
**Pages : **504
**ISBN Code: ** 1119541190
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**Summary:** A brand new, fully updated edition of a popular classic on matrix differential calculus with applications in statistics and econometrics This exhaustive, self-contained book on matrix theory and matrix differential calculus provides a treatment of matrix calculus based on differentials and shows how easy it is to use this theory once you have mastered the technique. Jan Magnus, who, along with the late Heinz Neudecker, pioneered the theory, develops it further in this new edition and provides many examples along the way to support it. Matrix calculus has become an essential tool for quantitative methods in a large number of applications, ranging from social and behavioral sciences to econometrics. It is still relevant and used today in a wide range of subjects such as the biosciences and psychology. Matrix Differential Calculus with Applications in Statistics and Econometrics, Third Edition contains all of the essentials of multivariable calculus with an emphasis on the use of differentials. It starts by presenting a concise, yet thorough overview of matrix algebra, then goes on to develop the theory of differentials. The rest of the text combines the theory and application of matrix differential calculus, providing the practitioner and researcher with both a quick review and a detailed reference. Fulfills the need for an updated and unified treatment of matrix differential calculus Contains many new examples and exercises based on questions asked of the author over the years Covers new developments in field and features new applications Written by a leading expert and pioneer of the theory Part of the Wiley Series in Probability and Statistics Matrix Differential Calculus With Applications in Statistics and Econometrics Third Edition is an ideal text for graduate students and academics studying the subject, as well as for postgraduates and specialists working in biosciences and psychology.

**Author : ** Roberto Moreno-Díaz,Franz Pichler,Alexis Quesada-Arencibia
**Publisher : **Springer
**Release Date : **2013-12-12
**Category: ** Computers
**Pages : **540
**ISBN Code: ** 3642538622
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**Summary:** The two-volume set LNCS 8111 and LNCS 8112 constitute the papers presented at the 14th International Conference on Computer Aided Systems Theory, EUROCAST 2013, held in February 2013 in Las Palmas de Gran Canaria, Spain. The total of 131 papers presented were carefully reviewed and selected for inclusion in the books. The contributions are organized in topical sections on modelling biological systems; systems theory and applications; intelligent information processing; theory and applications of metaheuristic algorithms; model-based system design, verification and simulation; process modeling simulation and system optimization; mobile and autonomous transportation systems; computer vision, sensing, image processing and medical applications; computer-based methods and virtual reality for clinical and academic medicine; digital signal processing methods and applications; mechatronic systems, robotics and marine robots; mobile computing platforms and technologies; systems applications.

**Author : ** Nathaniel Johnston
**Publisher : **Springer Nature
**Release Date : **2021-05-19
**Category: ** Mathematics
**Pages : **482
**ISBN Code: ** 3030528111
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**Summary:** This textbook emphasizes the interplay between algebra and geometry to motivate the study of linear algebra. Matrices and linear transformations are presented as two sides of the same coin, with their connection motivating inquiry throughout the book. By focusing on this interface, the author offers a conceptual appreciation of the mathematics that is at the heart of further theory and applications. Those continuing to a second course in linear algebra will appreciate the companion volume Advanced Linear and Matrix Algebra. Starting with an introduction to vectors, matrices, and linear transformations, the book focuses on building a geometric intuition of what these tools represent. Linear systems offer a powerful application of the ideas seen so far, and lead onto the introduction of subspaces, linear independence, bases, and rank. Investigation then focuses on the algebraic properties of matrices that illuminate the geometry of the linear transformations that they represent. Determinants, eigenvalues, and eigenvectors all benefit from this geometric viewpoint. Throughout, “Extra Topic” sections augment the core content with a wide range of ideas and applications, from linear programming, to power iteration and linear recurrence relations. Exercises of all levels accompany each section, including many designed to be tackled using computer software. Introduction to Linear and Matrix Algebra is ideal for an introductory proof-based linear algebra course. The engaging color presentation and frequent marginal notes showcase the author’s visual approach. Students are assumed to have completed one or two university-level mathematics courses, though calculus is not an explicit requirement. Instructors will appreciate the ample opportunities to choose topics that align with the needs of each classroom, and the online homework sets that are available through WeBWorK.

**Author : ** Zhong-Zhi Bai,Jian-Yu Pan
**Publisher : **SIAM
**Release Date : **2021-09-09
**Category: ** Mathematics
**Pages : **496
**ISBN Code: ** 1611976634
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**Summary:** This comprehensive book is presented in two parts; the first part introduces the basics of matrix analysis necessary for matrix computations, and the second part presents representative methods and the corresponding theories in matrix computations. Among the key features of the book are the extensive exercises at the end of each chapter. Matrix Analysis and Computations provides readers with the matrix theory necessary for matrix computations, especially for direct and iterative methods for solving systems of linear equations. It includes systematic methods and rigorous theory on matrix splitting iteration methods and Krylov subspace iteration methods, as well as current results on preconditioning and iterative methods for solving standard and generalized saddle-point linear systems. This book can be used as a textbook for graduate students as well as a self-study tool and reference for researchers and engineers interested in matrix analysis and matrix computations. It is appropriate for courses in numerical analysis, numerical optimization, data science, and approximation theory, among other topics

**Author : ** Piotr Antosik,Charles Swartz
**Publisher : **Springer
**Release Date : **2006-11-14
**Category: ** Mathematics
**Pages : **118
**ISBN Code: ** 3540392661
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**Author : ** Martha Abell,Emil Iacob,Alex Stokolos,Sharon Taylor,Sergey Tikhonov,Jiehua Zhu
**Publisher : **Springer Nature
**Release Date : **2019-10-21
**Category: ** Mathematics
**Pages : **373
**ISBN Code: ** 3030122778
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**Summary:** Different aspects of harmonic analysis, complex analysis, sampling theory, approximation theory and related topics are covered in this volume. The topics included are Fourier analysis, Padè approximation, dynamical systems and difference operators, splines, Christoffel functions, best approximation, discrepancy theory and Jackson-type theorems of approximation. The articles of this collection were originated from the International Conference in Approximation Theory, held in Savannah, GA in 2017, and organized by the editors of this volume.

**Author : ** Mario Paz,William Leigh
**Publisher : **Springer Science & Business Media
**Release Date : **2012-12-06
**Category: ** Technology & Engineering
**Pages : **321
**ISBN Code: ** 1461516110
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**Summary:** 7. 2 Element Stiffness Matrix of a Space Truss Local Coordinates 221 7. 3 Transformation of the Element Stiffness Matrix 223 7. 4 Element Axial Force 224 7. 5 Assemblage ofthe System Stiffness Matrix 225 7. 6 Problems 236 8 STATIC CONDENSATION AND SUBSTRUCTURING 8. 1 Introduction 239 8. 2 Static Condensation 239 8. 3 Substructuring 244 8. 4 Problems 259 9 INTRODUCTION TO FINITE ELEMENT MEmOD 9. 1 Introduction 261 9. 2 Plane Elasticity Problems 262 9. 3 Plate Bending 285 9. 4 Rectangular Finite Element for Plate Bending 285 9. 5 Problems 298 APPENDIX I Equivalent Nodal Forces 301 APPENDIXll Displacement Functions for Fixed-End Beams 305 GLOSSARY 309 SELECTED BmLIOGRAPHY 317 INDEX 319 ix Preface This is the first volume of a series of integrated textbooks for the analysis and design of structures. The series is projected to include a first volume in Matrix Structural Analysis to be followed by volumes in Structural Dynamics and Earthquake Engineering as well as other volumes dealing with specialized or advanced topics in the analysis and design of structures. An important objective in the preparation of these volumes is to integrate and unify the presentation using common notation, symbols and general format. Furthermore, all of these volumes will be using the same structural computer program, SAP2000, developed and maintained by Computers and Structures, Inc. , Berkeley, California.

**Author : ** James R. Schott
**Publisher : **John Wiley & Sons
**Release Date : **2016-05-31
**Category: ** Mathematics
**Pages : **552
**ISBN Code: ** 1119092469
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**Summary:** An up-to-date version of the complete, self-contained introduction to matrix analysis theory and practice Providing accessible and in-depth coverage of the most common matrix methods now used in statistical applications, Matrix Analysis for Statistics, Third Edition features an easy-to-follow theorem/proof format. Featuring smooth transitions between topical coverage, the author carefully justifies the step-by-step process of the most common matrix methods now used in statistical applications, including eigenvalues and eigenvectors; the Moore-Penrose inverse; matrix differentiation; and the distribution of quadratic forms. An ideal introduction to matrix analysis theory and practice, Matrix Analysis for Statistics, Third Edition features: • New chapter or section coverage on inequalities, oblique projections, and antieigenvalues and antieigenvectors • Additional problems and chapter-end practice exercises at the end of each chapter • Extensive examples that are familiar and easy to understand • Self-contained chapters for flexibility in topic choice • Applications of matrix methods in least squares regression and the analyses of mean vectors and covariance matrices Matrix Analysis for Statistics, Third Edition is an ideal textbook for upper-undergraduate and graduate-level courses on matrix methods, multivariate analysis, and linear models. The book is also an excellent reference for research professionals in applied statistics. James R. Schott, PhD, is Professor in the Department of Statistics at the University of Central Florida. He has published numerous journal articles in the area of multivariate analysis. Dr. Schott’s research interests include multivariate analysis, analysis of covariance and correlation matrices, and dimensionality reduction techniques.

**Author : ** Alan J. Laub
**Publisher : **SIAM
**Release Date : **2005-01-01
**Category: ** Mathematics
**Pages : **170
**ISBN Code: ** 0898717906
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**Summary:** Matrix Analysis for Scientists and Engineers provides a blend of undergraduate- and graduate-level topics in matrix theory and linear algebra that relieves instructors of the burden of reviewing such material in subsequent courses that depend heavily on the language of matrices. Consequently, the text provides an often-needed bridge between undergraduate-level matrix theory and linear algebra and the level of matrix analysis required for graduate-level study and research. The text is sufficiently compact that the material can be taught comfortably in a one-quarter or one-semester course. Throughout the book, the author emphasizes the concept of matrix factorization to provide a foundation for a later course in numerical linear algebra. The author addresses connections to differential and difference equations as well as to linear system theory and encourages instructors to augment these examples with other applications of their own choosing.

**Author : ** Randall Allemang
**Publisher : **Springer
**Release Date : **2014-05-05
**Category: ** Technology & Engineering
**Pages : **416
**ISBN Code: ** 3319047744
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**Summary:** This eighth volume of eight from the IMAC - XXXII Conference, brings together contributions to this important area of research and engineering. The collection presents early findings and case studies on fundamental and applied aspects of Structural Dynamics, including papers on: Linear Systems Substructure Modelling Adaptive Structures Experimental Techniques Analytical Methods Damage Detection Damping of Materials & Members Modal Parameter Identification Modal Testing Methods System Identification Active Control Modal Parameter Estimation Processing Modal Data

**Author : ** James E. Gentle
**Publisher : **Springer Science & Business Media
**Release Date : **2007-08-06
**Category: ** Mathematics
**Pages : **530
**ISBN Code: ** 0387708731
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**Summary:** Matrix algebra is one of the most important areas of mathematics for data analysis and for statistical theory. This much-needed work presents the relevant aspects of the theory of matrix algebra for applications in statistics. It moves on to consider the various types of matrices encountered in statistics, such as projection matrices and positive definite matrices, and describes the special properties of those matrices. Finally, it covers numerical linear algebra, beginning with a discussion of the basics of numerical computations, and following up with accurate and efficient algorithms for factoring matrices, solving linear systems of equations, and extracting eigenvalues and eigenvectors.

**Author : ** Brandon Dilworth,Michael Mains
**Publisher : **Springer Nature
**Release Date : **2020-10-22
**Category: ** Technology & Engineering
**Pages : **425
**ISBN Code: ** 3030477177
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**Summary:** Topics in Modal Analysis & Testing, Volume 8: Proceedings of the 38th IMAC, A Conference and Exposition on Structural Dynamics, 2020, the eighth volume of nine from the Conference, brings together contributions to this important area of research and engineering. The collection presents early findings and case studies on fundamental and applied aspects of Modal Analysis, including papers on: Operational Modal & Modal Analysis Applications Experimental Techniques Modal Analysis, Measurements & Parameter Estimation Modal Vectors & Modeling Basics of Modal Analysis Additive Manufacturing & Modal Testing of Printed Parts