Linear algebra is a living, active branch of mathematics which is central to almost all other areas of mathematics, both pure and applied, as well as computer science, the physical and social sciences, and engineering. It entails an extensive corpus of theoretical results as well as a large body of computational techniques. The book is intended to be used in one of several possible ways: (1) as a self-study guide; (2) as a textbook for a course in advanced linear algebra, either at the upper-class undergraduate level or at the first-year graduate level; or (3) as a reference book. It is also designed to prepare a student for the linear algebra portion of prelim exams or PhD qualifying exams. The volume is self-contained to the extent that it does not assume any previous formal knowledge of linear algebra, though the reader is assumed to have been exposed, at least informally, to some basic ideas and techniques, such as the solution of a small system of linear equations over the real numbers. More importantly, it does assume a seriousness of purpose and a modicum of mathematical sophistication. The book also contains over 1000 exercises, many of which are very challenging.

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This text for a second course in linear algebra, aimed at math majors and graduates, adopts a novel approach by banishing determinants to the end of the book and focusing on understanding the structure of linear operators on vector spaces. The author has taken unusual care to motivate concepts and to simplify proofs. For example, the book presents - without having defined determinants - a clean proof that every linear operator on a finite-dimensional complex vector space has an eigenvalue. The book starts by discussing vector spaces, linear independence, span, basics, and dimension. Students are introduced to inner-product spaces in the first half of the book and shortly thereafter to the finite- dimensional spectral theorem. A variety of interesting exercises in each chapter helps students understand and manipulate the objects of linear algebra. This second edition features new chapters on diagonal matrices, on linear functionals and adjoints, and on the spectral theorem; some sections, such as those on self-adjoint and normal operators, have been entirely rewritten; and hundreds of minor improvements have been made throughout the text.

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

This book is an extensively revised version of my textbook "¥esodot HaAlgebra HaLiniarit" (The Foundations of Linear Algebra) used at many universities in Israel. It is designed for a comprehensive one-year course in linear algebra (112 lecture hours) for mathematics majors. Therefore, I assume that the student already has a certain amount of mathematical background - including set theory, mathematical induction, basic analytic geometry, and elementary calculus - as wellas a modicum of mathematical sophistication. My intention is to provide not only a solid basis in the abstract theory of linear algebra, but also to provide examples of the application of this theory to other branches ofmathematics and computer science. Thus, for example, the introduction of finite fields is dictated by the needs of students studying algebraic coding theory as an immediate followup to their linear algebra studies. Many of the students studying linear algebra either are familiar with the care and feeding of computers before they begin their studies or are simultaneously en rolled in an introductory computer science course. Therefore, consideration of the more computational aspects of linear algebra - such as the solution of systems of linear equations and the calculation of eigenvalues - is delayed until all students are assumed able to write computer programs for this purpose. Beginning with Chap ter VII, there is an implicit assumption that the student has access to a personal computer and knows how to use it.

Linear Algebra Problem Book can be either the main course or the dessert for someone who needs linear algebraand today that means every user of mathematics. It can be used as the basis of either an official course or a program of private study. If used as a course, the book can stand by itself, or if so desired, it can be stirred in with a standard linear algebra course as the seasoning that provides the interest, the challenge, and the motivation that is needed by experienced scholars as much as by beginning students. The best way to learn is to do, and the purpose of this book is to get the reader to DO linear algebra. The approach is Socratic: first ask a question, then give a hint (if necessary), then, finally, for security and completeness, provide the detailed answer.

Covers a notably broad range of topics, including some topics not generally found in linear algebra books Contains a discussion of the basics of linear algebra

The companion title, Linear Algebra, has sold over 8,000 copies The writing style is very accessible The material can be covered easily in a one-year or one-term course Includes Noah Snyder's proof of the Mason-Stothers polynomial abc theorem New material included on product structure for matrices including descriptions of the conjugation representation of the diagonal group

Linear algebra is a living, active branch of mathematics which is central to almost all other areas of mathematics, both pure and applied, as well as to computer science, to the physical, biological, and social sciences, and to engineering. It encompasses an extensive corpus of theoretical results as well as a large and rapidly-growing body of computational techniques. Unfortunately, in the past decade, the content of linear algebra courses required to complete an undergraduate degree in mathematics has been depleted to the extent that they fail to provide a sufficient theoretical or computational background. Students are not only less able to formulate or even follow mathematical proofs, they are also less able to understand the mathematics of the numerical algorithms they need for applications. Certainly, the material presented in the average undergraduate course is insufficient for graduate study. This book is intended to fill the gap which has developed by providing enough theoretical and computational material to allow the advanced undergraduate or beginning graduate student to overcome this deficiency and be able to work independently or in advanced courses. The book is intended to be used either as a self-study guide, a textbook for a course in advanced linear algebra, or as a reference book. It is also designed to prepare a student for the linear algebra portion of prelim exams or PhD qualifying exams. The volume is self-contained to the extent that it does not assume any previous formal knowledge of linear algebra, though the reader is assumed to have been exposed, at least informally, to some of the basic ideas and techniques, such as manipulation of small matrices and the solution of small systems of linear equations over the real numbers. More importantly, it assumes a seriousness of purpose, considerable motivation, and a modicum of mathematical sophistication on the part of the reader. In the latest edition, new major theorems have been added, as well as many new examples. There are over 130 additional exercises and many of the previous exercises have been revised or rewritten. In addition, a large number of additional biographical notes and thumbnail portraits of mathematicians have been included.