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Scalar, Vector, and Matrix Mathematics

Author: Dennis S. Bernstein

Publisher: Princeton University Press

Published: 2018-02-27

Total Pages: 1593

ISBN-13: 0691176531

The essential reference book on matrices—now fully updated and expanded, with new material on scalar and vector mathematics Since its initial publication, this book has become the essential reference for users of matrices in all branches of engineering, science, and applied mathematics. In this revised and expanded edition, Dennis Bernstein combines extensive material on scalar and vector mathematics with the latest results in matrix theory to make this the most comprehensive, current, and easy-to-use book on the subject. Each chapter describes relevant theoretical background followed by specialized results. Hundreds of identities, inequalities, and facts are stated clearly and rigorously, with cross-references, citations to the literature, and helpful comments. Beginning with preliminaries on sets, logic, relations, and functions, this unique compendium covers all the major topics in matrix theory, such as transformations and decompositions, polynomial matrices, generalized inverses, and norms. Additional topics include graphs, groups, convex functions, polynomials, and linear systems. The book also features a wealth of new material on scalar inequalities, geometry, combinatorics, series, integrals, and more. Now more comprehensive than ever, Scalar, Vector, and Matrix Mathematics includes a detailed list of symbols, a summary of notation and conventions, an extensive bibliography and author index with page references, and an exhaustive subject index. Fully updated and expanded with new material on scalar and vector mathematics Covers the latest results in matrix theory Provides a list of symbols and a summary of conventions for easy and precise use Includes an extensive bibliography with back-referencing plus an author index

Introduction to Applied Linear Algebra

Author: Stephen Boyd

Publisher: Cambridge University Press

Published: 2018-06-07

Total Pages: 477

ISBN-13: 1316518965

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A groundbreaking introduction to vectors, matrices, and least squares for engineering applications, offering a wealth of practical examples.

Matrix Mathematics

Author: Dennis S. Bernstein

Publisher: Princeton University Press

Published: 2009-07-26

Total Pages: 1183

ISBN-13: 0691140391

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Each chapter in this book describes relevant background theory followed by specialized results. Hundreds of identities, inequalities, and matrix facts are stated clearly with cross references, citations to the literature, and illuminating remarks.

Scalar, Vector, and Matrix Mathematics

Author: Dennis S. Bernstein

Publisher: Princeton University Press

Published: 2018-02-27

Total Pages: 1600

ISBN-13: 1400888255

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Quantitative Economics with R

Author: Vikram Dayal

Publisher: Springer Nature

Published: 2020-02-03

Total Pages: 323

ISBN-13: 9811520356

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This book provides a contemporary treatment of quantitative economics, with a focus on data science. The book introduces the reader to R and RStudio, and uses expert Hadley Wickham’s tidyverse package for different parts of the data analysis workflow. After a gentle introduction to R code, the reader’s R skills are gradually honed, with the help of “your turn” exercises. At the heart of data science is data, and the book equips the reader to import and wrangle data, (including network data). Very early on, the reader will begin using the popular ggplot2 package for visualizing data, even making basic maps. The use of R in understanding functions, simulating difference equations, and carrying out matrix operations is also covered. The book uses Monte Carlo simulation to understand probability and statistical inference, and the bootstrap is introduced. Causal inference is illuminated using simulation, data graphs, and R code for applications with real economic examples, covering experiments, matching, regression discontinuity, difference-in-difference, and instrumental variables. The interplay of growth related data and models is presented, before the book introduces the reader to time series data analysis with graphs, simulation, and examples. Lastly, two computationally intensive methods—generalized additive models and random forests (an important and versatile machine learning method)—are introduced intuitively with applications. The book will be of great interest to economists—students, teachers, and researchers alike—who want to learn R. It will help economics students gain an intuitive appreciation of applied economics and enjoy engaging with the material actively, while also equipping them with key data science skills.

Matrices and Vector SPates

Author: William Brown

Publisher: CRC Press

Published: 1991-03-01

Total Pages: 338

ISBN-13: 9780824784195

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A textbook for a one-semester course in linear algebra for graduate or upper-level undergraduate students of mathematics and engineering. Employs a matrix perspective, and emphasizes training in definitions, theorems, and proofs. Annotation copyright Book News, Inc. Portland, Or.

Vectors, Matrices and Geometry

Author: K.T. Leung

Publisher: Hong Kong University Press

Published: 1994-08-01

Total Pages: 357

ISBN-13: 9622093604

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This book is the last volume of a three-book series written for Sixth Form students and first-year undergraduates. It introduces the important concepts of finite-dimensional vector spaces through the careful study of Euclidean geometry. In turn, methods of linear algebra are then used in the study of coordinate transformations through which a complete classification of conic sections and quadric surfaces is obtained. The book concludes with a detailed treatment of linear equations in n variables in the language of vectors and matrices. Illustrative examples are included in the main text and numerous exercises are given in each section. The other books in the series are Fundamental Concepts of Mathematics (published 1988) and Polynomials and Equations (published 1992).

Vectors and Matrices

Author: Cyrus Colton MacDuffee

Publisher: American Mathematical Soc.

Published: 1943-12-31

Total Pages: 203

ISBN-13: 1614440077

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In 1943, a course in linear algebra did not yet exist as a standard part of the undergraduate curriculum. It would be another twenty years before that would become common. It is, however, easy to identify the defining features of that course in this volume. Start with the idea of solving linear systems; change the point of view to that of transformations on vector spaces; recognize similarity as an essential classifying principle; and catalogue the canonical forms (Jordan normal form) of the transformations. All of this is here but with a decided, old-fashioned, algebraic accent—there is only one figure in the entire text.

Vectors and Matrices

Author: Pamela Liebeck

Publisher: Elsevier

Published: 2014-05-09

Total Pages: 193

ISBN-13: 1483280438

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Vectors and Matrices provides a progressive approach to vectors and matrices. The first half of this book is devoted to geometry, introducing matrices through its association with geometry mappings, while the rest of the chapters focus on the importance of matrices in non-geometric situations, such as the theory of linear equations and eigenvector theory. The power of eigenvector theory and its application to some problems in biology, probability, and genetics are also reviewed. Other topics include the product of scalar and vector, vector equation of a line, linear dependence, three-dimensional mappings, and orthogonal matrices. The transpose of a matrix and vector, rectangular matrices, inverse of a square matrix, and eigenvectors of a matrix are likewise emphasized in this text. This publication is beneficial to students and researchers conducting work on vectors and matrices.

Learning R

Author: Richard Cotton

Publisher: "O'Reilly Media, Inc."

Published: 2013-09-09

Total Pages: 400

ISBN-13: 1449357180

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Learn how to perform data analysis with the R language and software environment, even if you have little or no programming experience. With the tutorials in this hands-on guide, you’ll learn how to use the essential R tools you need to know to analyze data, including data types and programming concepts. The second half of Learning R shows you real data analysis in action by covering everything from importing data to publishing your results. Each chapter in the book includes a quiz on what you’ve learned, and concludes with exercises, most of which involve writing R code. Write a simple R program, and discover what the language can do Use data types such as vectors, arrays, lists, data frames, and strings Execute code conditionally or repeatedly with branches and loops Apply R add-on packages, and package your own work for others Learn how to clean data you import from a variety of sources Understand data through visualization and summary statistics Use statistical models to pass quantitative judgments about data and make predictions Learn what to do when things go wrong while writing data analysis code