Matrix Algebra : Theory, Computations and Applications in Statistics. 2nd ed. 2017

種類:

電子ブック

責任表示:

by James E. Gentle

出版情報:

Cham : Springer International Publishing : Imprint: Springer, 2017

著者名:

• Gentle, James E.
• SpringerLink (Online service)

シリーズ名:

Springer Texts in Statistics ;

ISBN:

9783319648675 [3319648675]    

注記:

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 -- Part II Applications in Data Analysis -- 8 Special Matrices and Operations Useful in Modeling andData Analysis -- 9 Selected Applications in Statistics -- Part III Numerical Methods and Software -- 10 Numerical Methods -- 11 Numerical Linear Algebra -- 12 Software for Numerical Linear Algebra -- Appendices and Back Matter -- Bibliography -- Index.
This textbook for graduate and advanced undergraduate students 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 the second edition of this very popular textbook provides essential updates and comprehensive coverage on critical topics in mathematics in data science and in statistical theory. Part I offers a self-contained description of relevant aspects of the theory 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. Part II considers various types of matrices encountered in statistics, such as

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