04615nam a22006135i 4500 978-3-031-42144-0 DE-He213 20251030111503.0 cr nn 008mamaa 240307s2024 sz | s |||| 0|eng d 9783031421440 978-3-031-42144-0 10.1007/978-3-031-42144-0 doi QA276-280 PBT bicssc MAT029000 bisacsh PBT thema Gentle, James E. author. aut http://id.loc.gov/vocabulary/relators/aut 72549 Matrix Algebra [electronic resource] : Theory, Computations and Applications in Statistics / by James E. Gentle. 3rd ed. 2024. Cham : Springer International Publishing : Imprint: Springer, 2024. XXXII, 693 p. 107 illus. online resource. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Springer Texts in Statistics, 2197-4136 Part I Linear Algebra -- 1 Basic Vector/Matrix Structure and Notation -- 2 Vectors and Vector Spaces -- 3 Basic Properties of Matrices -- 4 Vector/Matrix Derivatives and Integrals -- 5 Matrix Transformations and Factorizations -- 6 Solution of Linear Systems -- 7 Evaluation of Eigenvalues and Eigenvectors. 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 for various courses that emphasize computations. Statistics. 65982 Algebra. 1501 Mathematical statistics Data processing. 64750 Computer science Mathematics. 64041 Mathematical statistics. 67233 Mathematics Data processing. 65715 Statistical Theory and Methods. 72550 Algebra. 1501 Statistics and Computing. 66446 Probability and Statistics in Computer Science. 67234 Computational Mathematics and Numerical Analysis. 66073 SpringerLink (Online service) Springer Nature eBook Printed edition: 9783031421433 Printed edition: 9783031421457 Printed edition: 9783031424168 Printed edition: 9783031516450 Springer Texts in Statistics, 2197-4136 72551 https://doi.org/10.1007/978-3-031-42144-0 ZDB-2-SMA ZDB-2-SXMS 58148 58148