Matrix Algebra
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Matrix Algebra
Author: James E. Gentle
language: en
Publisher: Springer Science & Business Media
Release Date: 2007-08-06
Matrix algebra is one of the most important areas of mathematics for data analysis and for statistical theory. The first part of this book presents the relevant aspects of the theory of matrix algebra for applications in statistics. This part begins with the fundamental concepts of vectors and vector spaces, next covers the basic algebraic properties of matrices, then describes the analytic properties of vectors and matrices in the multivariate calculus, and finally discusses operations on matrices in solutions of linear systems and in eigenanalysis. This part is essentially self-contained. The second part of the book begins with a consideration of various types of matrices encountered in statistics, such as projection matrices and positive definite matrices, and describes the special properties of those matrices. The second part also describes some of the many applications of matrix theory in statistics, including linear models, multivariate analysis, and stochastic processes. The brief coverage in this part illustrates the matrix theory developed in the first part of the book. The first two parts of the book can be used as the text for a course in matrix algebra for statistics students, or as a supplementary text for various courses in linear models or multivariate statistics. The third part of this book covers numerical linear algebra. It begins with a discussion of the basics of numerical computations, and then describes accurate and efficient algorithms for factoring matrices, solving linear systems of equations, and extracting eigenvalues and eigenvectors. Although the book is not tied to any particular software system, it describes and gives examples of the use of modern computer software for numerical linear algebra. This part is essentially self-contained, although it assumes some ability to program in Fortran or C and/or the ability to use R/S-Plus or Matlab. This part of the book can be used as the text for a course in statistical computing, or as a supplementary text for various courses that emphasize computations. The book includes a large number of exercises with some solutions provided in an appendix.
Matrix Algebra
Author: Narayanan Krishnan Namboodiri
language: en
Publisher: SAGE Publications, Incorporated
Release Date: 1984-07
Conducted under the umbrella of Project Gunrunner, intended to stem the flow of firearms to Mexico, the Bureau of Alcohol, Tobacco, Firearms, and Explosives (ATF) ran a series of gun walking sting operations, including Operations Wide Receiver and Operation Fast & Furious. The government allowed licensed gun dealers to sell weapons to illegal straw buyers so that they could continue to track the firearms as they were transferred to higher-level traffickers and key figures in Mexican cartels.Motivated by a sense of patriotic duty, Tucson gun dealer and author Mike Detty alerted the local ATF office when he was first approached by suspected cartel associates. Detty made the commitment and assumed the risks involved to help the feds make their case, often selling guns to these thugs from his home in the dead of night. Originally informed that the investigation would last just weeks, Detty s undercover involvement in Operation Wide Receiver, the precursor to Operation Fast & Furious, which was by far the largest gun walking probe, stretched on for an astonishing and dangerous three years.Though the case took several twists and turns, perhaps the cruelest turn was his betrayal by the very agency he risked everything to help.
Matrix Algebra
Author: Karim M. Abadir
language: en
Publisher: Cambridge University Press
Release Date: 2005-08-22
Matrix Algebra is the first volume of the Econometric Exercises Series. It contains exercises relating to course material in matrix algebra that students are expected to know while enrolled in an (advanced) undergraduate or a postgraduate course in econometrics or statistics. The book contains a comprehensive collection of exercises, all with full answers. But the book is not just a collection of exercises; in fact, it is a textbook, though one that is organized in a completely different manner than the usual textbook. The volume can be used either as a self-contained course in matrix algebra or as a supplementary text.