04210nam a22005295i 4500001001800000003000900018005001700027007001500044008004100059020001800100024003500118050001400153072001600167072002300183072001500206100007800221245012000299250001800419264007500437300004700512336002600559337002600585338003600611347002400647490004500671505031200716520199901028650001603027650001303043650004603056650003503102650002903137650003403166650003603200650001303236650003003249650005203279650005403331710003403385773002603419776003603445776003603481776003603517776003603553830004503589856004603634978-3-031-42144-0DE-He21320251030111503.0cr nn 008mamaa240307s2024    sz |    s    |||| 0|eng d  a97830314214407 a10.1007/978-3-031-42144-02doi 4aQA276-280 7aPBT2bicssc 7aMAT0290002bisacsh 7aPBT2thema1 aGentle, James E.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut10aMatrix Algebrah[electronic resource] :bTheory, Computations and Applications in Statistics /cby James E. Gentle.  a3rd ed. 2024. 1aCham :bSpringer International Publishing :bImprint: Springer,c2024.  aXXXII, 693 p. 107 illus.bonline resource.  atextbtxt2rdacontent  acomputerbc2rdamedia  aonline resourcebcr2rdacarrier  atext filebPDF2rda1 aSpringer Texts in Statistics,x2197-41360 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.  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. 0aStatistics. 0aAlgebra. 0aMathematical statisticsxData processing. 0aComputer sciencexMathematics. 0aMathematical statistics. 0aMathematicsxData processing.14aStatistical Theory and Methods.24aAlgebra.24aStatistics and Computing.24aProbability and Statistics in Computer Science.24aComputational Mathematics and Numerical Analysis.2 aSpringerLink (Online service)0 tSpringer Nature eBook08iPrinted edition:z978303142143308iPrinted edition:z978303142145708iPrinted edition:z978303142416808iPrinted edition:z9783031516450 0aSpringer Texts in Statistics,x2197-413640uhttps://doi.org/10.1007/978-3-031-42144-0