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Matrix Mathematics


Matrix Mathematics
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Matrix Mathematics


Matrix Mathematics
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Author : Dennis S. Bernstein
language : en
Publisher: Princeton University Press
Release Date : 2009-07-06

Matrix Mathematics written by Dennis S. Bernstein and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-07-06 with Mathematics categories.


When first published in 2005, Matrix Mathematics quickly became the essential reference book for users of matrices in all branches of engineering, science, and applied mathematics. In this fully updated and expanded edition, the author brings together the latest results on matrix theory to make this the most complete, current, and easy-to-use book on matrices. Each chapter describes relevant background theory followed by specialized results. Hundreds of identities, inequalities, and matrix facts are stated clearly and rigorously with cross references, citations to the literature, and illuminating remarks. Beginning with preliminaries on sets, functions, and relations,Matrix Mathematics covers all of the major topics in matrix theory, including matrix transformations; polynomial matrices; matrix decompositions; generalized inverses; Kronecker and Schur algebra; positive-semidefinite matrices; vector and matrix norms; the matrix exponential and stability theory; and linear systems and control theory. Also included are a detailed list of symbols, a summary of notation and conventions, an extensive bibliography and author index with page references, and an exhaustive subject index. This significantly expanded edition of Matrix Mathematics features a wealth of new material on graphs, scalar identities and inequalities, alternative partial orderings, matrix pencils, finite groups, zeros of multivariable transfer functions, roots of polynomials, convex functions, and matrix norms. Covers hundreds of important and useful results on matrix theory, many never before available in any book Provides a list of symbols and a summary of conventions for easy use Includes an extensive collection of scalar identities and inequalities Features a detailed bibliography and author index with page references Includes an exhaustive subject index with cross-referencing



Matrix Mathematics


Matrix Mathematics
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Author : Stephan Ramon Garcia
language : en
Publisher: Cambridge University Press
Release Date : 2023-05-25

Matrix Mathematics written by Stephan Ramon Garcia and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-05-25 with Mathematics categories.


Using a modern matrix-based approach, this rigorous second course in linear algebra helps upper-level undergraduates in mathematics, data science, and the physical sciences transition from basic theory to advanced topics and applications. Its clarity of exposition together with many illustrations, 900+ exercises, and 350 conceptual and numerical examples aid the student's understanding. Concise chapters promote a focused progression through essential ideas. Topics are derived and discussed in detail, including the singular value decomposition, Jordan canonical form, spectral theorem, QR factorization, normal matrices, Hermitian matrices, and positive definite matrices. Each chapter ends with a bullet list summarizing important concepts. New to this edition are chapters on matrix norms and positive matrices, many new sections on topics including interpolation and LU factorization, 300+ more problems, many new examples, and color-enhanced figures. Prerequisites include a first course in linear algebra and basic calculus sequence. Instructor's resources are available.



Scalar Vector And Matrix Mathematics


Scalar Vector And Matrix Mathematics
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Author : Dennis S. Bernstein
language : en
Publisher: Princeton University Press
Release Date : 2018-02-27

Scalar Vector And Matrix Mathematics written by Dennis S. Bernstein and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-02-27 with Mathematics categories.


The essential reference book on matrices—now fully updated and expanded, with new material on scalar and vector mathematics Since its initial publication, this book has become the essential reference for users of matrices in all branches of engineering, science, and applied mathematics. In this revised and expanded edition, Dennis Bernstein combines extensive material on scalar and vector mathematics with the latest results in matrix theory to make this the most comprehensive, current, and easy-to-use book on the subject. Each chapter describes relevant theoretical background followed by specialized results. Hundreds of identities, inequalities, and facts are stated clearly and rigorously, with cross-references, citations to the literature, and helpful comments. Beginning with preliminaries on sets, logic, relations, and functions, this unique compendium covers all the major topics in matrix theory, such as transformations and decompositions, polynomial matrices, generalized inverses, and norms. Additional topics include graphs, groups, convex functions, polynomials, and linear systems. The book also features a wealth of new material on scalar inequalities, geometry, combinatorics, series, integrals, and more. Now more comprehensive than ever, Scalar, Vector, and Matrix Mathematics includes a detailed list of symbols, a summary of notation and conventions, an extensive bibliography and author index with page references, and an exhaustive subject index. Fully updated and expanded with new material on scalar and vector mathematics Covers the latest results in matrix theory Provides a list of symbols and a summary of conventions for easy and precise use Includes an extensive bibliography with back-referencing plus an author index



Hands On Matrix Algebra Using R Active And Motivated Learning With Applications


Hands On Matrix Algebra Using R Active And Motivated Learning With Applications
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Author : Hrishikesh D Vinod
language : en
Publisher: World Scientific Publishing Company
Release Date : 2011-03-28

Hands On Matrix Algebra Using R Active And Motivated Learning With Applications written by Hrishikesh D Vinod and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-03-28 with Mathematics categories.


This is the first book of its kind which teaches matrix algebra, allowing the student to learn the material by actually working with matrix objects in modern computer environment of R. Instead of a calculator, R is a vastly more powerful free software and graphics system.The book provides a comprehensive overview of matrix theory without being bogged down in proofs or tedium. The reader can check each matrix result with numerical examples of exactly what they mean and understand their implications. The book does not shy away from advanced topics, especially the ones with practical applications.



Matrix Mathematics


Matrix Mathematics
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Author : Dennis S. Bernstein
language : en
Publisher: Princeton University Press
Release Date : 2009-07-26

Matrix Mathematics written by Dennis S. Bernstein and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-07-26 with Mathematics categories.


Each chapter in this book describes relevant background theory followed by specialized results. Hundreds of identities, inequalities, and matrix facts are stated clearly with cross references, citations to the literature, and illuminating remarks.



Matrix Algebra For Social Scientists


Matrix Algebra For Social Scientists
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Author : Paul Horst
language : en
Publisher:
Release Date : 1961

Matrix Algebra For Social Scientists written by Paul Horst and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1961 with Matrices categories.




Matrix Algebra


Matrix Algebra
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Author : James E. Gentle
language : en
Publisher: Springer Nature
Release Date : 2024-03-07

Matrix Algebra written by James E. Gentle and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-03-07 with Mathematics categories.


This book presents the theory of matrix algebra for statistical applications, explores various types of matrices encountered in statistics, and covers numerical linear algebra. Matrix algebra is one of the most important areas of mathematics in data science and in statistical theory, and previous editions had essential updates and comprehensive coverage on critical topics in mathematics. This 3rd edition offers a self-contained description of relevant aspects of matrix algebra for applications in statistics. It begins with fundamental concepts of vectors and vector spaces; covers basic algebraic properties of matrices and analytic properties of vectors and matrices in multivariate calculus; and concludes with a discussion on operations on matrices, in solutions of linear systems and in eigenanalysis. It also includes discussions of the R software package, with numerous examples and exercises. Matrix Algebra considers various types of matrices encountered in statistics, such as projection matrices and positive definite matrices, and describes special properties of those matrices; as well as describing various applications of matrix theory in statistics, including linear models, multivariate analysis, and stochastic processes. It begins with a discussion of the basics of numerical computations and goes on to describe accurate and efficient algorithms for factoring matrices, how to solve linear systems of equations, and the extraction of eigenvalues and eigenvectors. It covers numerical linear algebra—one of the most important subjects in the field of statistical computing. The content includes greater emphases on R, and extensive coverage of statistical linear models. Matrix Algebra is ideal for graduate and advanced undergraduate students, or as a supplementary text for courses in linear models or multivariate statistics. It’s also ideal for use in a course in statistical computing, or as a supplementary text forvarious courses that emphasize computations.



Matrix Algebra And Its Applications To Statistics And Econometrics


Matrix Algebra And Its Applications To Statistics And Econometrics
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Author : Calyampudi Radhakrishna Rao
language : en
Publisher: World Scientific
Release Date : 1998

Matrix Algebra And Its Applications To Statistics And Econometrics written by Calyampudi Radhakrishna Rao and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Mathematics categories.


"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, 2000



Mathematics Of Big Data


Mathematics Of Big Data
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Author : Jeremy Kepner
language : en
Publisher: MIT Press
Release Date : 2018-07-17

Mathematics Of Big Data written by Jeremy Kepner and has been published by MIT Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-07-17 with Computers categories.


The first book to present the common mathematical foundations of big data analysis across a range of applications and technologies. Today, the volume, velocity, and variety of data are increasing rapidly across a range of fields, including Internet search, healthcare, finance, social media, wireless devices, and cybersecurity. Indeed, these data are growing at a rate beyond our capacity to analyze them. The tools—including spreadsheets, databases, matrices, and graphs—developed to address this challenge all reflect the need to store and operate on data as whole sets rather than as individual elements. This book presents the common mathematical foundations of these data sets that apply across many applications and technologies. Associative arrays unify and simplify data, allowing readers to look past the differences among the various tools and leverage their mathematical similarities in order to solve the hardest big data challenges. The book first introduces the concept of the associative array in practical terms, presents the associative array manipulation system D4M (Dynamic Distributed Dimensional Data Model), and describes the application of associative arrays to graph analysis and machine learning. It provides a mathematically rigorous definition of associative arrays and describes the properties of associative arrays that arise from this definition. Finally, the book shows how concepts of linearity can be extended to encompass associative arrays. Mathematics of Big Data can be used as a textbook or reference by engineers, scientists, mathematicians, computer scientists, and software engineers who analyze big data.



Matrix Algebra Useful For Statistics


Matrix Algebra Useful For Statistics
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Author : Shayle R. Searle
language : en
Publisher: John Wiley & Sons
Release Date : 2006-03-20

Matrix Algebra Useful For Statistics written by Shayle R. Searle and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-03-20 with Mathematics categories.


WILEY-INTERSCIENCE PAPERBACK SERIES The Wiley-Interscience Paperback Series consists of selected booksthat have been made more accessible to consumers in an effort toincrease global appeal and general circulation. With these newunabridged softcover volumes, Wiley hopes to extend the lives ofthese works by making them available to future generations ofstatisticians, mathematicians, and scientists. "This book is intended to teach useful matrix algebra to 'students,teachers, consultants, researchers, and practitioners' in'statistics and other quantitative methods'.The author concentrateson practical matters, and writes in a friendly and informal style .. . this is a useful and enjoyable book to have at hand." -Biometrics This book is an easy-to-understand guide to matrix algebra and itsuses in statistical analysis. The material is presented in anexplanatory style rather than the formal theorem-proof format. Thisself-contained text includes numerous applied illustrations,numerical examples, and exercises.