Pdf ebook: Introduction to Matrix Analysis and Applications

Pdf download ebook Introduction to Matrix Analysis and Applications

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

  • Author : N.a
  • Publisher: Springer Science & Business Media
  • ISBN: 3319041509
  • Genre: Mathematics
  • Number of Pages: 332
  • Language: English
  • Views: 1986
  • Downloads: 1986
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Description: 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.


Pdf ebook: Introduction to Linear and Matrix Algebra

Pdf download ebook Introduction to Linear and Matrix Algebra

Summary: This textbook emphasizes the interplay between algebra and geometry to motivate the study of linear algebra. Matrices and linear transformations are presen

  • Author : Nathaniel Johnston
  • Publisher: Springer Nature
  • ISBN: 3030528111
  • Genre: Mathematics
  • Number of Pages: 482
  • Language: English
  • Views: 349
  • Downloads: 349
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Description: 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.


Pdf ebook: Applied Linear Algebra and Matrix Analysis

Pdf download ebook Applied Linear Algebra and Matrix Analysis

Summary: This new book offers a fresh approach to matrix and linear algebra by providing a balanced blend of applications, theory, and computation, while highlighti

  • Author : Thomas S. Shores
  • Publisher: Springer Science & Business Media
  • ISBN: 0387489479
  • Genre: Mathematics
  • Number of Pages: 384
  • Language: English
  • Views: 710
  • Downloads: 710
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Description: This new book offers a fresh approach to matrix and linear algebra by providing a balanced blend of applications, theory, and computation, while highlighting their interdependence. Intended for a one-semester course, Applied Linear Algebra and Matrix Analysis places special emphasis on linear algebra as an experimental science, with numerous examples, computer exercises, and projects. While the flavor is heavily computational and experimental, the text is independent of specific hardware or software platforms. Throughout the book, significant motivating examples are woven into the text, and each section ends with a set of exercises.


Pdf ebook: Matrix Algebra for Linear Models

Pdf download ebook Matrix Algebra for Linear Models

Summary: A self-contained introduction to matrix analysis theory andapplications in the field of statistics Comprehensive in scope, Matrix Algebra for Linear Models

  • Author : Marvin H. J. Gruber
  • Publisher: John Wiley & Sons
  • ISBN: 111860881X
  • Genre: Mathematics
  • Number of Pages: 392
  • Language: English
  • Views: 1130
  • Downloads: 1130
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Description: A self-contained introduction to matrix analysis theory andapplications in the field of statistics Comprehensive in scope, Matrix Algebra for Linear Modelsoffers a succinct summary of matrix theory and its relatedapplications to statistics, especially linear models. The bookprovides a unified presentation of the mathematical properties andstatistical applications of matrices in order to define andmanipulate data. Written for theoretical and applied statisticians, the bookutilizes multiple numerical examples to illustrate key ideas,methods, and techniques crucial to understanding matrixalgebra’s application in linear models. Matrix Algebra forLinear Models expertly balances concepts and methods allowingfor a side-by-side presentation of matrix theory and its linearmodel applications. Including concise summaries on each topic, thebook also features: Methods of deriving results from the properties of eigenvaluesand the singular value decomposition Solutions to matrix optimization problems for obtaining moreefficient biased estimators for parameters in linear regressionmodels A section on the generalized singular value decomposition Multiple chapter exercises with selected answers to enhanceunderstanding of the presented material Matrix Algebra for Linear Models is an ideal textbook foradvanced undergraduate and graduate-level courses on statistics,matrices, and linear algebra. The book is also an excellentreference for statisticians, engineers, economists, and readersinterested in the linear statistical model.


Pdf ebook: Matrix Theory and Applications with MATLAB

Pdf download ebook Matrix Theory and Applications with MATLAB

Summary: Designed for use in a second course on linear algebra, Matrix Theory and Applications with MATLAB covers the basics of the subject-from a review of matrix

  • Author : Darald J. Hartfiel
  • Publisher: CRC Press
  • ISBN: 1482285630
  • Genre: Mathematics
  • Number of Pages: 384
  • Language: English
  • Views: 925
  • Downloads: 925
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Description: Designed for use in a second course on linear algebra, Matrix Theory and Applications with MATLAB covers the basics of the subject-from a review of matrix algebra through vector spaces to matrix calculus and unitary similarity-in a presentation that stresses insight, understanding, and applications. Among its most outstanding features is the integration of MATLAB throughout the text. Each chapter includes a MATLAB subsection that discusses the various commands used to do the computations in that section and offers code for the graphics and some algorithms used in the text. All of the material is presented from a matrix point of view with enough rigor for students to learn to compose arguments and proofs and adjust the material to cover other problems. The treatment includes optional subsections covering applications, and the final chapters move beyond basic matrix theory to discuss more advanced topics, such as decompositions, positive definite matrices, graphics, and topology. Filled with illustrations, examples, and exercises that reinforce understanding, Matrix Theory and Applications with MATLAB allows readers to experiment and visualize results in a way that no other text does. Its rigor, use of MATLAB, and focus on applications better prepares them to use the material in their future work and research, to extend the material, and perhaps obtain new results of their own.


Pdf ebook: Introduction to Matrix Theory

Pdf download ebook Introduction to Matrix Theory

Summary: In economic modeling and planning, as well as in business, most problems are linear, or approximated by linear models. Such problems are solved by matrix m

  • Author : Ferenc Szidarovszky,Sándor Molnár
  • Publisher: World Scientific Publishing Company
  • ISBN: 9813102608
  • Genre: Mathematics
  • Number of Pages: 512
  • Language: English
  • Views: 1756
  • Downloads: 1756
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Description: In economic modeling and planning, as well as in business, most problems are linear, or approximated by linear models. Such problems are solved by matrix methods, so the material presented in this book is essential to these fields.


Pdf ebook: Introduction to the Theory and Applications of Functional Differential Equations

Pdf download ebook Introduction to the Theory and Applications of Functional Differential Equations

Summary: This book covers the most important issues in the theory of functional differential equations and their applications for both deterministic and stochastic

  • Author : V. Kolmanovskii,A. Myshkis
  • Publisher: Springer Science & Business Media
  • ISBN: 9401719659
  • Genre: Mathematics
  • Number of Pages: 648
  • Language: English
  • Views: 594
  • Downloads: 594
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Description: This book covers the most important issues in the theory of functional differential equations and their applications for both deterministic and stochastic cases. Among the subjects treated are qualitative theory, stability, periodic solutions, optimal control and estimation, the theory of linear equations, and basic principles of mathematical modelling. The work, which treats many concrete problems in detail, gives a good overview of the entire field and will serve as a stimulating guide to further research. Audience: This volume will be of interest to researchers and (post)graduate students working in analysis, and in functional analysis in particular. It will also appeal to mathematical engineers, industrial mathematicians, mathematical system theoreticians and mathematical modellers.


Pdf ebook: Computational Matrix Analysis

Pdf download ebook Computational Matrix Analysis

Summary: Using an approach that author Alan Laub calls "matrix analysis for grown-ups," this new textbook introduces fundamental concepts of numerical linear algebr

  • Author : Alan J. Laub
  • Publisher: SIAM
  • ISBN: 1611972213
  • Genre: Mathematics
  • Number of Pages: 157
  • Language: English
  • Views: 526
  • Downloads: 526
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Description: Using an approach that author Alan Laub calls "matrix analysis for grown-ups," this new textbook introduces fundamental concepts of numerical linear algebra and their application to solving certain numerical problems arising in state-space control and systems theory. It is written for advanced undergraduate and beginning graduate students and can be used as a follow-up to Matrix Analysis for Scientists and Engineers (SIAM, 2005), a compact single-semester introduction to matrix analysis for engineers and computational scientists by the same author. Computational Matrix Analysis provides readers with a one-semester introduction to numerical linear algebra; an introduction to statistical condition estimation in book form for the first time; and an overview of certain computational problems in control and systems theory. The book features a number of elements designed to help students learn to use numerical linear algebra in day-to-day computing or research, including a brief review of matrix analysis, including notation, and an introduction to finite (IEEE) arithmetic; discussion and examples of conditioning, stability, and rounding analysis; an introduction to mathematical software topics related to numerical linear algebra; a thorough introduction to Gaussian elimination, along with condition estimation techniques; coverage of linear least squares, with orthogonal reduction and QR factorization; variants of the QR algorithm; and applications of the discussed algorithms.


Pdf ebook: Matrix Analysis and Applied Linear Algebra

Pdf download ebook Matrix Analysis and Applied Linear Algebra

Summary: Matrix Analysis and Applied Linear Algebra is an honest math text that circumvents the traditional definition-theorem-proof format that has bored students

  • Author : Carl D. Meyer
  • Publisher: SIAM
  • ISBN: 0898719518
  • Genre: Mathematics
  • Number of Pages: 718
  • Language: English
  • Views: 1447
  • Downloads: 1447
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Description: 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.


Pdf ebook: Introduction to Random Matrices

Pdf download ebook Introduction to Random Matrices

Summary: Modern developments of Random Matrix Theory as well as pedagogical approaches to the standard core of the discipline are surprisingly hard to find in a wel

  • Author : Giacomo Livan,Marcel Novaes,Pierpaolo Vivo
  • Publisher: Springer
  • ISBN: 3319708856
  • Genre: Science
  • Number of Pages: 124
  • Language: English
  • Views: 765
  • Downloads: 765
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Description: Modern developments of Random Matrix Theory as well as pedagogical approaches to the standard core of the discipline are surprisingly hard to find in a well-organized, readable and user-friendly fashion. This slim and agile book, written in a pedagogical and hands-on style, without sacrificing formal rigor fills this gap. It brings Ph.D. students in Physics, as well as more senior practitioners, through the standard tools and results on random matrices, with an eye on most recent developments that are not usually covered in introductory texts. The focus is mainly on random matrices with real spectrum.The main guiding threads throughout the book are the Gaussian Ensembles. In particular, Wigner’s semicircle law is derived multiple times to illustrate several techniques (e.g., Coulomb gas approach, replica theory).Most chapters are accompanied by Matlab codes (stored in an online repository) to guide readers through the numerical check of most analytical results.


Pdf ebook: Linear Algebra and Matrix Analysis for Statistics

Pdf download ebook Linear Algebra and Matrix Analysis for Statistics

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

  • Author : Sudipto Banerjee,Anindya Roy
  • Publisher: CRC Press
  • ISBN: 1482248247
  • Genre: Mathematics
  • Number of Pages: 580
  • Language: English
  • Views: 349
  • Downloads: 349
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Description: 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.


Pdf ebook: Matrix Theory and Applications for Scientists and Engineers

Pdf download ebook Matrix Theory and Applications for Scientists and Engineers

Summary: In this comprehensive text on matrix theory and its applications, Graham explores the underlying principles as well as the numerous applications of the var

  • Author : Alexander Graham
  • Publisher: Courier Dover Publications
  • ISBN: 0486832651
  • Genre: Mathematics
  • Number of Pages: 304
  • Language: English
  • Views: 1382
  • Downloads: 1382
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Description: In this comprehensive text on matrix theory and its applications, Graham explores the underlying principles as well as the numerous applications of the various concepts presented. Includes numerous problems with solutions. 1979 edition.


Pdf ebook: Numerical Matrix Analysis

Pdf download ebook Numerical Matrix Analysis

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

  • Author : Ilse C. F. Ipsen
  • Publisher: SIAM
  • ISBN: 089871768X
  • Genre: Algebra
  • Number of Pages: 128
  • Language: English
  • Views: 1593
  • Downloads: 1593
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Description: 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.


Pdf ebook: Matrix Analysis for Scientists and Engineers

Pdf download ebook Matrix Analysis for Scientists and Engineers

Summary: Matrix Analysis for Scientists and Engineers provides a blend of undergraduate- and graduate-level topics in matrix theory and linear algebra that relieves

  • Author : Alan J. Laub
  • Publisher: SIAM
  • ISBN: 0898717906
  • Genre: Mathematics
  • Number of Pages: 170
  • Language: English
  • Views: 451
  • Downloads: 451
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Description: 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.


Pdf ebook: Matrix Algebra

Pdf download ebook Matrix Algebra

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

  • Author : James E. Gentle
  • Publisher: Springer Science & Business Media
  • ISBN: 0387708731
  • Genre: Mathematics
  • Number of Pages: 530
  • Language: English
  • Views: 462
  • Downloads: 462
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Description: 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.


Pdf ebook: An Introduction to Queueing Theory

Pdf download ebook An Introduction to Queueing Theory

Summary: The present textbook contains the recordsof a two–semester course on que- ing theory, including an introduction to matrix–analytic methods. This course

  • Author : L. Breuer,Dieter Baum
  • Publisher: Springer Science & Business Media
  • ISBN: 1402036310
  • Genre: Mathematics
  • Number of Pages: 272
  • Language: English
  • Views: 1221
  • Downloads: 1221
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Description: The present textbook contains the recordsof a two–semester course on que- ing theory, including an introduction to matrix–analytic methods. This course comprises four hours oflectures and two hours of exercises per week andhas been taughtattheUniversity of Trier, Germany, for about ten years in - quence. The course is directed to last year undergraduate and?rst year gr- uate students of applied probability and computer science, who have already completed an introduction to probability theory. Its purpose is to present - terial that is close enough to concrete queueing models and their applications, while providing a sound mathematical foundation for the analysis of these. Thus the goal of the present book is two–fold. On the one hand, students who are mainly interested in applications easily feel bored by elaborate mathematical questions in the theory of stochastic processes. The presentation of the mathematical foundations in our courses is chosen to cover only the necessary results, which are needed for a solid foundation of the methods of queueing analysis. Further, students oriented - wards applications expect to have a justi?cation for their mathematical efforts in terms of immediate use in queueing analysis. This is the main reason why we have decided to introduce new mathematical concepts only when they will be used in the immediate sequel. On the other hand, students of applied probability do not want any heur- tic derivations just for the sake of yielding fast results for the model at hand.


Pdf ebook: Matrix Algebra and Its Applications to Statistics and Econometrics

Pdf download ebook Matrix Algebra and Its Applications to Statistics and Econometrics

Summary: Written by two top statisticians with experience in teaching matrix methods for applications in statistics, econometrics and related areas, this book provi

  • Author : C Radhakrishna Rao,M Bhaskara Rao
  • Publisher: World Scientific
  • ISBN: 981449691X
  • Genre: Mathematics
  • Number of Pages: 556
  • Language: English
  • Views: 1246
  • Downloads: 1246
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Description: Written by two top statisticians with experience in teaching matrix methods for applications in statistics, econometrics and related areas, this book provides a comprehensive treatment of the latest techniques in matrix algebra. A well-balanced approach to discussing the mathematical theory and applications to problems in other areas is an attractive feature of the book. It can be used as a textbook in courses on matrix algebra for statisticians, econometricians and mathematicians as well. Some of the new developments of linear models are given in some detail using results of matrix algebra. Contents:Vector SpacesUnitary and Euclidean SpacesLinear Transformations and MatricesCharacteristics of MatricesFactorization of MatricesOperations on MatricesProjectors and Idempotent OperatorsGeneralized InversesMajorizationInequalities for EigenvaluesMatrix ApproximationsOptimization Problems in Statistics and EconometricsQuadratic SubspacesInequalities with Applications in StatisticsNon-negative MatricesMiscellaneous Complements Readership: Graduate students, researchers and scientists in economics, biology, engineering and physics. keywords:Matrices;Matrix Inequalities;Matrix Approximations;Singular Value;Decomposition;Generalized Matrix Inverse;Spectral Theory;Statistical Applications;Econometric Models;Growth Models “I recommend this book for its extensive coverage of topics not easily found elsewhere and for its focus on applications.” Zentralblatt MATH “The book is an excellent source on linear algebra, matrix theory and applications in statistics and econometrics, and is unique in many ways. I recommend it to anyone interested in these disciplines, and especially in how they benefit from one another.” Statistical Papers “… there is a category of readers that would certainly benefit from this book: statisticians who have obtained their knowledge of matrix algebra in a piecemeal fashion and now want to systematically improve their knowledge of the theory and their skills in manipulating matrices.” Journal of the American Statistical Association


Pdf ebook: Applications of Combinatorial Matrix Theory to Laplacian Matrices of Graphs

Pdf download ebook Applications of Combinatorial Matrix Theory to Laplacian Matrices of Graphs

Summary: On the surface, matrix theory and graph theory seem like very different branches of mathematics. However, adjacency, Laplacian, and incidence matrices are

  • Author : Jason J. Molitierno
  • Publisher: CRC Press
  • ISBN: 1439863393
  • Genre: Computers
  • Number of Pages: 425
  • Language: English
  • Views: 503
  • Downloads: 503
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Description: On the surface, matrix theory and graph theory seem like very different branches of mathematics. However, adjacency, Laplacian, and incidence matrices are commonly used to represent graphs, and many properties of matrices can give us useful information about the structure of graphs.Applications of Combinatorial Matrix Theory to Laplacian Matrices o


Pdf ebook: Introduction to Matrix Analytic Methods in Stochastic Modeling

Pdf download ebook Introduction to Matrix Analytic Methods in Stochastic Modeling

Summary: Matrix analytic methods are popular as modeling tools because they give one the ability to construct and analyze a wide class of queuing models in a unifie

  • Author : G. Latouche,V. Ramaswami
  • Publisher: SIAM
  • ISBN: 9780898719734
  • Genre: Markov processes
  • Number of Pages: 334
  • Language: English
  • Views: 824
  • Downloads: 824
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Description: Matrix analytic methods are popular as modeling tools because they give one the ability to construct and analyze a wide class of queuing models in a unified and algorithmically tractable way. The authors present the basic mathematical ideas and algorithms of the matrix analytic theory in a readable, up-to-date, and comprehensive manner. In the current literature, a mixed bag of techniques is used-some probabilistic, some from linear algebra, and some from transform methods. Here, many new proofs that emphasize the unity of the matrix analytic approach are included.


Pdf ebook: Applied and Computational Matrix Analysis

Pdf download ebook Applied and Computational Matrix Analysis

Summary: This volume presents recent advances in the field of matrix analysis based on contributions at the MAT-TRIAD 2015 conference. Topics covered include interv

  • Author : Natália Bebiano
  • Publisher: Springer
  • ISBN: 331949984X
  • Genre: Mathematics
  • Number of Pages: 347
  • Language: English
  • Views: 1577
  • Downloads: 1577
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Description: 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.