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| Author | : Stephen Boyd |
| Publisher | : Cambridge University Press |
| Total Pages | : 477 |
| Release | : 2018-06-07 |
| Genre | : Business & Economics |
| ISBN | : 1316518965 |
A groundbreaking introduction to vectors, matrices, and least squares for engineering applications, offering a wealth of practical examples.
| Author | : James E. Gentle |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 536 |
| Release | : 2007-07-27 |
| Genre | : Computers |
| ISBN | : 0387708723 |
Matrix algebra is one of the most important areas of mathematics for data analysis and for statistical theory. This much-needed work presents the relevant aspects of the theory of matrix algebra for applications in statistics. It moves on to consider the various types of matrices encountered in statistics, such as projection matrices and positive definite matrices, and describes the special properties of those matrices. Finally, it covers numerical linear algebra, beginning with a discussion of the basics of numerical computations, and following up with accurate and efficient algorithms for factoring matrices, solving linear systems of equations, and extracting eigenvalues and eigenvectors.
| Author | : Nathaniel Johnston |
| Publisher | : Springer Nature |
| Total Pages | : 482 |
| Release | : 2021-05-19 |
| Genre | : Mathematics |
| ISBN | : 3030528111 |
This textbook emphasizes the interplay between algebra and geometry to motivate the study of linear algebra. Matrices and linear transformations are presented as two sides of the same coin, with their connection motivating inquiry throughout the book. By focusing on this interface, the author offers a conceptual appreciation of the mathematics that is at the heart of further theory and applications. Those continuing to a second course in linear algebra will appreciate the companion volume Advanced Linear and Matrix Algebra. Starting with an introduction to vectors, matrices, and linear transformations, the book focuses on building a geometric intuition of what these tools represent. Linear systems offer a powerful application of the ideas seen so far, and lead onto the introduction of subspaces, linear independence, bases, and rank. Investigation then focuses on the algebraic properties of matrices that illuminate the geometry of the linear transformations that they represent. Determinants, eigenvalues, and eigenvectors all benefit from this geometric viewpoint. Throughout, “Extra Topic” sections augment the core content with a wide range of ideas and applications, from linear programming, to power iteration and linear recurrence relations. Exercises of all levels accompany each section, including many designed to be tackled using computer software. Introduction to Linear and Matrix Algebra is ideal for an introductory proof-based linear algebra course. The engaging color presentation and frequent marginal notes showcase the author’s visual approach. Students are assumed to have completed one or two university-level mathematics courses, though calculus is not an explicit requirement. Instructors will appreciate the ample opportunities to choose topics that align with the needs of each classroom, and the online homework sets that are available through WeBWorK.
| Author | : Nick Fieller |
| Publisher | : CRC Press |
| Total Pages | : 208 |
| Release | : 2018-09-03 |
| Genre | : Mathematics |
| ISBN | : 1315360055 |
A Thorough Guide to Elementary Matrix Algebra and Implementation in R Basics of Matrix Algebra for Statistics with R provides a guide to elementary matrix algebra sufficient for undertaking specialized courses, such as multivariate data analysis and linear models. It also covers advanced topics, such as generalized inverses of singular and rectangular matrices and manipulation of partitioned matrices, for those who want to delve deeper into the subject. The book introduces the definition of a matrix and the basic rules of addition, subtraction, multiplication, and inversion. Later topics include determinants, calculation of eigenvectors and eigenvalues, and differentiation of linear and quadratic forms with respect to vectors. The text explores how these concepts arise in statistical techniques, including principal component analysis, canonical correlation analysis, and linear modeling. In addition to the algebraic manipulation of matrices, the book presents numerical examples that illustrate how to perform calculations by hand and using R. Many theoretical and numerical exercises of varying levels of difficulty aid readers in assessing their knowledge of the material. Outline solutions at the back of the book enable readers to verify the techniques required and obtain numerical answers. Avoiding vector spaces and other advanced mathematics, this book shows how to manipulate matrices and perform numerical calculations in R. It prepares readers for higher-level and specialized studies in statistics.
| Author | : Karim M. Abadir |
| Publisher | : Cambridge University Press |
| Total Pages | : 472 |
| Release | : 2005-08-22 |
| Genre | : Business & Economics |
| ISBN | : 9780521822893 |
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.
| Author | : Narayanan Krishnan Namboodiri |
| Publisher | : SAGE Publications, Incorporated |
| Total Pages | : 106 |
| Release | : 1984-07 |
| Genre | : Mathematics |
| ISBN | : |
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.
| Author | : Robert R. Stoll |
| Publisher | : Courier Corporation |
| Total Pages | : 290 |
| Release | : 2012-10-17 |
| Genre | : Mathematics |
| ISBN | : 0486623181 |
Advanced undergraduate and first-year graduate students have long regarded this text as one of the best available works on matrix theory in the context of modern algebra. Teachers and students will find it particularly suited to bridging the gap between ordinary undergraduate mathematics and completely abstract mathematics. The first five chapters treat topics important to economics, psychology, statistics, physics, and mathematics. Subjects include equivalence relations for matrixes, postulational approaches to determinants, and bilinear, quadratic, and Hermitian forms in their natural settings. The final chapters apply chiefly to students of engineering, physics, and advanced mathematics. They explore groups and rings, canonical forms for matrixes with respect to similarity via representations of linear transformations, and unitary and Euclidean vector spaces. Numerous examples appear throughout the text.
| Author | : Philip N. Klein |
| Publisher | : |
| Total Pages | : 530 |
| Release | : 2013-07 |
| Genre | : Algebras, Linear |
| ISBN | : 9780615856735 |
An engaging introduction to vectors and matrices and the algorithms that operate on them, intended for the student who knows how to program. Mathematical concepts and computational problems are motivated by applications in computer science. The reader learns by "doing," writing programs to implement the mathematical concepts and using them to carry out tasks and explore the applications. Examples include: error-correcting codes, transformations in graphics, face detection, encryption and secret-sharing, integer factoring, removing perspective from an image, PageRank (Google's ranking algorithm), and cancer detection from cell features. A companion web site, codingthematrix.com provides data and support code. Most of the assignments can be auto-graded online. Over two hundred illustrations, including a selection of relevant "xkcd" comics. Chapters: "The Function," "The Field," "The Vector," "The Vector Space," "The Matrix," "The Basis," "Dimension," "Gaussian Elimination," "The Inner Product," "Special Bases," "The Singular Value Decomposition," "The Eigenvector," "The Linear Program" A new edition of this text, incorporating corrections and an expanded index, has been issued as of September 4, 2013, and will soon be available on Amazon.
| Author | : David A. Harville |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 639 |
| Release | : 2008-06-27 |
| Genre | : Mathematics |
| ISBN | : 0387783563 |
A knowledge of matrix algebra is a prerequisite for the study of much of modern statistics, especially the areas of linear statistical models and multivariate statistics. This reference book provides the background in matrix algebra necessary to do research and understand the results in these areas. Essentially self-contained, the book is best-suited for a reader who has had some previous exposure to matrices. Solultions to the exercises are available in the author's "Matrix Algebra: Exercises and Solutions."
| Author | : Ivan Savov |
| Publisher | : |
| Total Pages | : 596 |
| Release | : 2020-10-25 |
| Genre | : MATHEMATICS |
| ISBN | : 9780992001025 |
This textbook covers the material for an undergraduate linear algebra course: vectors, matrices, linear transformations, computational techniques, geometric constructions, and theoretical foundations. The explanations are given in an informal conversational tone. The book also contains 100+ problems and exercises with answers and solutions. A special feature of this textbook is the prerequisites chapter that covers topics from high school math, which are necessary for learning linear algebra. The presence of this chapter makes the book suitable for beginners and the general audience-readers need not be math experts to read this book. Another unique aspect of the book are the applications chapters (Ch 7, 8, and 9) that discuss applications of linear algebra to engineering, computer science, economics, chemistry, machine learning, and even quantum mechanics.
