Applied Matrix Algebra In The Statistical Sciences
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Applied Matrix Algebra In The Statistical Sciences
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Author : Alexander Basilevsky
language : en
Publisher: Courier Corporation
Release Date : 2005-12-27
Applied Matrix Algebra In The Statistical Sciences written by Alexander Basilevsky and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-12-27 with Mathematics categories.
This comprehensive text covers both applied and theoretical branches of matrix algebra in the statistical sciences. It also provides a bridge between linear algebra and statistical models. Appropriate for advanced undergraduate and graduate students, the self-contained treatment also constitutes a handy reference for researchers. The only mathematical background necessary is a sound knowledge of high school mathematics and a first course in statistics. Consisting of two interrelated parts, this volume begins with the basic structure of vectors and vector spaces. The latter part emphasizes the diverse properties of matrices and their associated linear transformations--and how these, in turn, depend upon results derived from linear vector spaces. An overview of introductory concepts leads to more advanced topics such as latent roots and vectors, generalized inverses, and nonnegative matrices. Each chapter concludes with a section on real-world statistical applications, plus exercises that offer concrete examples of the applications of matrix algebra.
Applied Matrix Algebra In The Statistical Sciences
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Author : Alexander Basilevsky
language : en
Publisher: Courier Corporation
Release Date : 2013-01-18
Applied Matrix Algebra In The Statistical Sciences written by Alexander Basilevsky and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-01-18 with Mathematics categories.
This comprehensive text offers teachings relevant to both applied and theoretical branches of matrix algebra and provides a bridge between linear algebra and statistical models. Appropriate for advanced undergraduate and graduate students. 1983 edition.
Linear Algebra And Matrix Analysis For Statistics
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Author : Sudipto Banerjee
language : en
Publisher: CRC Press
Release Date : 2014-06-06
Linear Algebra And Matrix Analysis For Statistics written by Sudipto Banerjee and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-06-06 with Mathematics categories.
Linear Algebra and Matrix Analysis for Statistics 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 is as self-contained as possible, assuming no prior knowledge of linear algebra. The authors first address the rudimentary mechanics of linear systems using Gaussian elimination and the resulting decompositions. They introduce Euclidean vector spaces using less abstract concepts and make connections to systems of linear equations wherever possible. After illustrating the importance of the rank of a matrix, they discuss complementary subspaces, oblique projectors, orthogonality, orthogonal projections and projectors, and orthogonal reduction. The text then shows how the theoretical concepts developed are handy in analyzing solutions for linear systems. The authors also explain how determinants are useful for characterizing and deriving properties concerning matrices and linear systems. They then cover eigenvalues, eigenvectors, singular value decomposition, Jordan decomposition (including a proof), quadratic forms, and Kronecker and Hadamard products. The book concludes with accessible treatments of advanced topics, such as linear iterative systems, convergence of matrices, more general vector spaces, linear transformations, and Hilbert spaces.
Matrix Algebra And Its Applications To Statistics And Econometrics
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Author : Calyampudi Radhakrishna Rao
language : en
Publisher: World Scientific
Release Date : 1998-07-10
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 1998-07-10 with Mathematics categories.
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.
Introduction To Applied Linear Algebra
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Author : Stephen Boyd
language : en
Publisher: Cambridge University Press
Release Date : 2018-06-07
Introduction To Applied Linear Algebra written by Stephen Boyd 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 2018-06-07 with Business & Economics categories.
A groundbreaking introduction to vectors, matrices, and least squares for engineering applications, offering a wealth of practical examples.
Matrix Algebra From A Statistician S Perspective
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Author : David A. Harville
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-06-27
Matrix Algebra From A Statistician S Perspective written by David A. Harville and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-06-27 with Mathematics categories.
A knowledge of matrix algebra is a prerequisite for the study of much of modern statistics, especially the areas of linear statistical models and multivariate statistics. This reference book provides the background in matrix algebra necessary to do research and understand the results in these areas. Essentially self-contained, the book is best-suited for a reader who has had some previous exposure to matrices. Solultions to the exercises are available in the author's "Matrix Algebra: Exercises and Solutions."
Matrix Algebra
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Author : James E. Gentle
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-08-06
Matrix Algebra written by James E. Gentle and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-08-06 with Mathematics categories.
Matrix algebra is one of the most important areas of mathematics for data analysis and for statistical theory. The first part of this book presents the relevant aspects of the theory of matrix algebra for applications in statistics. This part begins with the fundamental concepts of vectors and vector spaces, next covers the basic algebraic properties of matrices, then describes the analytic properties of vectors and matrices in the multivariate calculus, and finally discusses operations on matrices in solutions of linear systems and in eigenanalysis. This part is essentially self-contained. The second part of the book begins with a consideration of various types of matrices encountered in statistics, such as projection matrices and positive definite matrices, and describes the special properties of those matrices. The second part also describes some of the many applications of matrix theory in statistics, including linear models, multivariate analysis, and stochastic processes. The brief coverage in this part illustrates the matrix theory developed in the first part of the book. The first two parts of the book can be used as the text for a course in matrix algebra for statistics students, or as a supplementary text for various courses in linear models or multivariate statistics. The third part of this book covers numerical linear algebra. It begins with a discussion of the basics of numerical computations, and then describes accurate and efficient algorithms for factoring matrices, solving linear systems of equations, and extracting eigenvalues and eigenvectors. Although the book is not tied to any particular software system, it describes and gives examples of the use of modern computer software for numerical linear algebra. This part is essentially self-contained, although it assumes some ability to program in Fortran or C and/or the ability to use R/S-Plus or Matlab. This part of the book can be used as the text for a course in statistical computing, or as a supplementary text for various courses that emphasize computations. The book includes a large number of exercises with some solutions provided in an appendix.
Linear Algebra And Its Applications With R
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Author : Ruriko Yoshida
language : en
Publisher: CRC Press
Release Date : 2024-08-26
Linear Algebra And Its Applications With R written by Ruriko Yoshida and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-08-26 with Business & Economics categories.
The book developed from the need to teach a linear algebra course to students focused on data science and bioinformatics programs. This textbook provides students a theoretical basis which can then be applied to the practical R and Python problems, providing the tools needed for real-world applications.
Matrix Tricks For Linear Statistical Models
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Author : Simo Puntanen
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-08-24
Matrix Tricks For Linear Statistical Models written by Simo Puntanen and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-08-24 with Mathematics categories.
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.
An Introduction To Applied Matrix Analysis
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Author : Xiao Qing Jin
language : en
Publisher: World Scientific Publishing Company
Release Date : 2016-05-30
An Introduction To Applied Matrix Analysis written by Xiao Qing Jin 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 2016-05-30 with Mathematics categories.
It is well known that most problems in science and engineering eventually progress into matrix problems. This book gives an elementary introduction to applied matrix theory and it also includes some new results obtained in recent years.The book consists of eight chapters. It includes perturbation and error analysis; the conjugate gradient method for solving linear systems; preconditioning techniques; and least squares algorithms based on orthogonal transformations, etc. The last two chapters include some latest development in the area. In Chap. 7, we construct optimal preconditioners for functions of matrices. More precisely, let f be a function of matrices. Given a matrix A, there are two choices of constructing optimal preconditioners for f(A). Properties of these preconditioners are studied for different functions. In Chap. 8, we study the Bottcher-Wenzel conjecture and discuss related problems.This is a textbook for senior undergraduate or junior graduate students majoring in science and engineering. The material is accessible to students who, in various disciplines, have basic linear algebra, calculus, numerical analysis, and computing knowledge. The book is also useful to researchers in computational science who are interested in applied matrix theory.