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020 _a9783031421440
_9978-3-031-42144-0
024 7 _a10.1007/978-3-031-42144-0
_2doi
050 4 _aQA276-280
072 7 _aPBT
_2bicssc
072 7 _aMAT029000
_2bisacsh
072 7 _aPBT
_2thema
100 1 _aGentle, James E.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_972549
245 1 0 _aMatrix Algebra
_h[electronic resource] :
_bTheory, Computations and Applications in Statistics /
_cby James E. Gentle.
250 _a3rd ed. 2024.
264 1 _aCham :
_bSpringer International Publishing :
_bImprint: Springer,
_c2024.
300 _aXXXII, 693 p. 107 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aSpringer Texts in Statistics,
_x2197-4136
505 0 _aPart 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.
520 _aThis 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.
650 0 _aStatistics.
_965982
650 0 _aAlgebra.
_91501
650 0 _aMathematical statistics
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650 0 _aComputer science
_xMathematics.
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650 0 _aMathematical statistics.
_967233
650 0 _aMathematics
_xData processing.
_965715
650 1 4 _aStatistical Theory and Methods.
_972550
650 2 4 _aAlgebra.
_91501
650 2 4 _aStatistics and Computing.
_966446
650 2 4 _aProbability and Statistics in Computer Science.
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650 2 4 _aComputational Mathematics and Numerical Analysis.
_966073
710 2 _aSpringerLink (Online service)
773 0 _tSpringer Nature eBook
776 0 8 _iPrinted edition:
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776 0 8 _iPrinted edition:
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776 0 8 _iPrinted edition:
_z9783031424168
776 0 8 _iPrinted edition:
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830 0 _aSpringer Texts in Statistics,
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856 4 0 _uhttps://doi.org/10.1007/978-3-031-42144-0
912 _aZDB-2-SMA
912 _aZDB-2-SXMS
999 _c58148
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