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Matrix Algebra

Author: James E. Gentle
Publisher: Springer
ISBN: 3319648675
Size: 24.54 MB
Format: PDF, ePub
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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.

Matrix Algebra

Author: James E. Gentle
Publisher: Springer Science & Business Media
ISBN: 0387708723
Size: 27.36 MB
Format: PDF, ePub, Docs
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This much-needed work presents, among other things, the relevant aspects of the theory of matrix algebra for applications in statistics. Written in an informal style, it addresses computational issues and places more emphasis on applications than existing texts.

Matrix Algebra

Author: James E. Gentle
Publisher: Springer Science & Business Media
ISBN: 0387708731
Size: 37.54 MB
Format: PDF, Kindle
View: 324
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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.

Numerical Linear Algebra For Applications In Statistics

Author: James E. Gentle
Publisher: Springer Science & Business Media
ISBN: 1461206235
Size: 21.14 MB
Format: PDF, ePub
View: 3495
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Accurate and efficient computer algorithms for factoring matrices, solving linear systems of equations, and extracting eigenvalues and eigenvectors. Regardless of the software system used, the book describes and gives examples of the use of modern computer software for numerical linear algebra. It begins with a discussion of the basics of numerical computations, and then describes the relevant properties of matrix inverses, factorisations, matrix and vector norms, and other topics in linear algebra. The book is essentially self- contained, with the topics addressed constituting the essential material for an introductory course in statistical computing. Numerous exercises allow the text to be used for a first course in statistical computing or as supplementary text for various courses that emphasise computations.

Linear Algebra And Matrix Analysis For Statistics

Author: Sudipto Banerjee
Publisher: CRC Press
ISBN: 1420095382
Size: 44.63 MB
Format: PDF, Mobi
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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 Exercises And Solutions

Author: David A. Harville
Publisher: Springer Science & Business Media
ISBN: 1461301815
Size: 67.59 MB
Format: PDF, Mobi
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This book contains over 300 exercises and solutions that together cover a wide variety of topics in matrix algebra. They can be used for independent study or in creating a challenging and stimulating environment that encourages active engagement in the learning process. The requisite background is some previous exposure to matrix algebra of the kind obtained in a first course. The exercises are those from an earlier book by the same author entitled Matrix Algebra From a Statistician's Perspective. They have been restated (as necessary) to stand alone, and the book includes extensive and detailed summaries of all relevant terminology and notation. The coverage includes topics of special interest and relevance in statistics and related disciplines, as well as standard topics. The overlap with exercises available from other sources is relatively small. This collection of exercises and their solutions will be a useful reference for students and researchers in matrix algebra. It will be of interest to mathematicians and statisticians.

Applied Linear Algebra And Matrix Analysis

Author: Thomas S. Shores
Publisher: Springer
ISBN: 3319747487
Size: 48.41 MB
Format: PDF, Mobi
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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.

Matrices

Author: Denis Serre
Publisher: Springer Science & Business Media
ISBN: 9781441976833
Size: 47.52 MB
Format: PDF, ePub, Mobi
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In this book, Denis Serre begins by providing a clean and concise introduction to the basic theory of matrices. He then goes on to give many interesting applications of matrices to different aspects of mathematics and also other areas of science and engineering. With forty percent new material, this second edition is significantly different from the first edition. Newly added topics include: • Dunford decomposition, • tensor and exterior calculus, polynomial identities, • regularity of eigenvalues for complex matrices, • functional calculus and the Dunford–Taylor formula, • numerical range, • Weyl's and von Neumann’s inequalities, and • Jacobi method with random choice. The book mixes together algebra, analysis, complexity theory and numerical analysis. As such, this book will provide many scientists, not just mathematicians, with a useful and reliable reference. It is intended for advanced undergraduate and graduate students with either applied or theoretical goals. This book is based on a course given by the author at the École Normale Supérieure de Lyon.

Matrices With Applications In Statistics

Author: Franklin A. Graybill
Publisher: Duxbury Press
ISBN: 9780534401313
Size: 35.79 MB
Format: PDF, Docs
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Part of the Duxbury Classic series, Franklin A. Graybill’s MATRICES WITH APPLICATIONS TO STATISTICS focuses primarily on matrices as they relate to areas of multivariate analysis and the linear model. This seminal work is a time tested, authoritative resource for both students and researchers.

Matrix Algebra

Author: Karim M. Abadir
Publisher: Cambridge University Press
ISBN: 9780521822893
Size: 20.17 MB
Format: PDF, Kindle
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A stand-alone textbook in matrix algebra for econometricians and statisticians - advanced undergraduates, postgraduates and teachers.