Linear Algebra Filetype Pdf

[Landerico Benson]

LinearAlgebra: Gateway to Mathematics uses linear algebra as a vehicle to introduce students to the inner workings of mathematics. The structures and techniques of mathematics in turn provide an accessible framework to illustrate the powerful and beautiful results about vector spaces and linear transformations.

The unifying concepts of linear algebra reveal the analogies among three primary examples: Euclidean spaces, function spaces, and collections of matrices. Students are gently introduced to abstractions of higher mathematics through discussions of the logical structure of proofs, the need to translate terminology into notation, and efficient ways to discover and present proofs. Application of linear algebra and concrete examples tie the abstract concepts to familiar objects from algebra, geometry, calculus, and everyday life.

Students will finish a course using this text with an understanding of the basic results of linear algebra and an appreciation of the beauty and utility of mathematics. They will also be fortified with a degree of mathematical maturity required for subsequent courses in abstract algebra, real analysis, and elementary topology. Students who have prior background in dealing with the mechanical operations of vectors and matrices will benefit from seeing this material placed in a more general context.

Roughly the first third of the book covers the basic material of a first course in linear algebra. The remaining chapters are devoted to applications drawn from vector calculus, numerical analysis, control theory, complex analysis, convexity and functional analysis. In particular, fixed point theorems, extremal problems, matrix equations, zero location and eigenvalue location problems, and matrices with nonnegative entries are discussed. Appendices on useful facts from analysis and supplementary information from complex function theory are also provided for the convenience of the reader.

In this new edition, most of the chapters in the first edition have been revised, some extensively. The revisions include changes in a number of proofs, either to simplify the argument, to make the logic clearer or, on occasion, to sharpen the result. New introductory sections on linear programming, extreme points for polyhedra and a Nevanlinna-Pick interpolation problem have been added, as have some very short introductory sections on the mathematics behind Google, Drazin inverses, band inverses and applications of SVD together with a number of new exercises.

Linear Algebra in Action ... occupies a position on my primary bookshelf - the place where I keep the books I will want to have handy when I am working on mathematics. ... Whereas most books in mathematics do not have much personality, Dym's book does: it is enlivened with quotes (many of them from baseball, some witty, some off the wall, all worthy) and is written in a manner that seems almost to have been transcribed word for word from an oral lecture. The voice of the "teacher" is present throughout the text. ... Dym's book is ... a singular and significant addition to the literature, with many important topics treated here in one volume. The emphasis on examples will be appreciated by many. ... It is gratifying to see the inclusion of Linear Algebra in Action in the high quality AMS Graduate Studies in Mathematics series, as it is an indirect affirmation of a subject that is both important and vibrant. Dym's book should go far in bringing serious matrix analysis to the next generation of mathematicians.

Changing the order of coverage of the main sections would likely disrupt the careful development of theory in the first three chapters. End-of-chapter Topics can be covered in any order, or omitted. In the Preface, the author suggests going through the text (exclusive of Topics) in order and suggests the rate at which that can be done. He also marks some sections as optional, so that they can be skipped to devote time to other parts of the text.

The material is logically ordered and divided into five chapters, but Chapter Three is much longer than any other chapter. It could be split into two chapters, the second one on orthogonality and its applications.

The author not only provides .pdf files of the book and solutions manual with helpful links, but also includes a lab manual that introduces the interested reader to Python and Sage. Besides those, he includes extra problems with solutions, an introduction to proofs, and an article on matrix arithmetic. Professor Hefferon tries hard to motivate every topic he covers and almost always succeeds. He is to be commended and appreciated for doing everything he could to help students and instructors to benefit from and make maximal use of his text. Even when it is not used as the text for a course, it can serve as a useful reference.

The book covers the standard material for an introductory course in linear algebra. The material is standard in that the topics covered are Gaussian reduction, vector spaces, linear maps, determinants, and eigenvalues and eigenvectors. The...read more

The book covers the standard material for an introductory course in linear algebra. The material is standard in that the topics covered are Gaussian reduction, vector spaces, linear maps, determinants, and eigenvalues and eigenvectors. The approach is developmental, the topics are covered in a comprehensive fashion, and the mathematical language of the book is very rigorous and proof-based. Nearly everything is proven either in the main text or in the exercises, which is helpful for readers who are trying to bring more rigor to their mathematical thinking and mathematical maturity.

The book is well balanced, substantial yet concise and has extensive exercise sets, with levels of difficulty varying from routine verifications to challenging problems, with worked answers and detailed solutions to all exercises. Each chapter closes with a selection of related special topics, usually applications to real world examples from physics, biology, economics, probability and abstract algebra that could be assigned as individual or group projects or could be presented in class. These special topics, such as crystals, stable populations, electrical networks, dimensional analysis, voting paradoxes and so on, together with the many interesting applications throughout the text, make this book more valuable than the average undergraduate linear algebra textbook.

On the web page of the author beamer slides for classroom use are available, that draw from the text source with respect to the notations, the numbering of theorems etc, but contain different examples than in the book. The web page also hosts a lab manual for computer work (using Sage) and links to a repository with the latex source files.

3a8082e126