
Author 
Georgi E. Shilov 
ISBN10 
9780486135045 
Year 
20120426 
Pages 
387 
Language 
en 
Publisher 
Courier Corporation 
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Covers determinants, linear spaces, systems of linear equations, linear functions of a vector argument, coordinate transformations, the canonical form of the matrix of a linear operator, bilinear and quadratic forms, and more.

Author 
A. G. Hamilton 
ISBN10 
0521310423 
Year 
1989 
Pages 
328 
Language 
en 
Publisher 
Cambridge University Press 
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Emphasis is placed on applications in preference to more theoretical aspects throughout this readable introduction to linear algebra for specialists as well as nonspecialists. An expanded version of A First Course in Linear Algebra.

Author 
Harvey E. Rose 
ISBN10 
376436792X 
Year 
20021001 
Pages 
250 
Language 
en 
Publisher 
Springer Science & Business Media 
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In algebra, an entity is called linear if it can be expressed in terms of addition, and multiplication by a scalar; a linear expression is a sum of scalar multiples of the entities under consideration. Also, an operation is called linear if it preserves addition, and multiplication by a scalar. For example, if A and Bare 2 x 2 real matrices, v is a (row) vector in the real plane, and c is a real number, then v(A + B) = vA + vB and (cv)A = c(vA), that is, the process of applying a matrix to a vector is linear. Linear Algebra is the study of properties and systems which preserve these two operations, and the following pages present the basic theory and results of this important branch of pure mathematics. There are many books on linear algebra in the bookshops and libraries of the world, so why write another? A number of excellent texts were written about fifty years ago (see the bibliography); in the intervening period the 'style' of math ematical presentation has changed. Also, some of the more modern texts have concentrated on applications both inside and outside mathematics. There is noth ing wrong with this approach; these books serve a very useful purpose. But linear algebra contains some fine pure mathematics and so a modern text taking the pure mathematician's viewpoint was thought to be worthwhile.

Author 
Serge Lang 
ISBN10 
0387964126 
Year 
19870126 
Pages 
285 
Language 
en 
Publisher 
Springer Science & Business Media 
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"Linear Algebra" is intended for a oneterm course at the junior or senior level. It begins with an exposition of the basic theory of vector spaces and proceeds to explain the fundamental structure theorem for linear maps, including eigenvectors and eigenvalues, quadratic and hermitian forms, diagnolization of symmetric, hermitian, and unitary linear maps and matrices, triangulation, and Jordan canonical form. The book also includes a useful chapter on convex sets and the finitedimensional KreinMilman theorem. The presentation is aimed at the student who has already had some exposure to the elementary theory of matrices, determinants and linear maps. However the book is logically selfcontained. In this new edition, many parts of the book have been rewritten and reorganized, and new exercises have been added.

Author 
Ravindra B. Bapat 
ISBN10 
9781447127383 
Year 
20120129 
Pages 
167 
Language 
en 
Publisher 
Springer Science & Business Media 
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Linear Algebra and Linear Models comprises a concise and rigorous introduction to linear algebra required for statistics followed by the basic aspects of the theory of linear estimation and hypothesis testing. The emphasis is on the approach using generalized inverses. Topics such as the multivariate normal distribution and distribution of quadratic forms are included. For this third edition, the material has been reorganised to develop the linear algebra in the first six chapters, to serve as a first course on linear algebra that is especially suitable for students of statistics or for those looking for a matrix theoretic approach to the subject. Other key features include: coverage of topics such as rank additivity, inequalities for eigenvalues and singular values; a new chapter on linear mixed models; over seventy additional problems on rank: the matrix rank is an important and rich topic with connections to many aspects of linear algebra such as generalized inverses, idempotent matrices and partitioned matrices. This text is aimed primarily at advanced undergraduate and firstyear graduate students taking courses in linear algebra, linear models, multivariate analysis and design of experiments. A wealth of exercises, complete with hints and solutions, help to consolidate understanding. Researchers in mathematics and statistics will also find the book a useful source of results and problems.

Author 
Larry Smith 
ISBN10 
0387984550 
Year 
19980528 
Pages 
454 
Language 
en 
Publisher 
Springer Science & Business Media 
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This popular and successful text was originally written for a onesemester course in linear algebra at the sophomore undergraduate level. Consequently, the book deals almost exclusively with real finite dimensional vector spaces, but in a setting and formulation that permits easy generalisation to abstract vector spaces. A wide selection of examples of vector spaces and linear transformation is presented to serve as a testing ground for the theory. In the second edition, a new chapter on Jordan normal form was added which reappears here in expanded form as the second goal of this new edition, after the principal axis theorem. To achieve these goals in one semester it is necessary to follow a straight path, but this is compensated by a wide selection of examples and exercises. In addition, the author includes an introduction to invariant theory to show that linear algebra alone is incapable of solving these canonical forms problems. A compact, but mathematically clean introduction to linear algebra with particular emphasis on topics in abstract algebra, the theory of differential equations, and group representation theory.

Author 
T.A. Whitelaw 
ISBN10 
0751401595 
Year 
19910401 
Pages 
288 
Language 
en 
Publisher 
CRC Press 
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This popular textbook was thoughtfully and specifically tailored to introducing undergraduate students to linear algebra. The second edition has been carefully revised to improve upon its already successful format and approach. In particular, the author added a chapter on quadratic forms, making this one of the most comprehensive introductory texts on linear algebra.

Author 
Vivek Sahai 
ISBN10 
0849324262 
Year 
20020501 
Pages 
208 
Language 
en 
Publisher 
CRC Press 
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This book presents a concise, comprehensive introduction to the fundamentals of linear algebra. The authors develop the subject in a manner accessible to readers of varied backgrounds. The material requires only very basic algebra and a rudimentary knowledge of matrices and determinants as prerequisites, but the text includes an introductory chapter containing most of the foundational material required. Linear Algebra begins with the basic concepts of vector spaces, subspace, basis, and dimension. Although the authors emphasize finite dimensional vector spaces, they also include examples of infinite dimensional vector spaces to highlight the differences between the two classes. The treatment then moves to the analysis of a single linear operator on a finite dimensional vector space, including discussions on characterizing diagonizable and triangulable operators. It uses the concept of generalized eigenvectors to obtain an inductive procedure for constructing a Jordan basis for a triangulable linear operator and again uses an algorithmic approach to the rational canonical form. Subsequent discussions focus on finite dimensional inner product spaces and nonnegative operators, isometries, and polar and singularvalue decomposition. The final chapter explores bilinear forms and extends the results of inner product spaces to bilinear spaces. Numerous examples and exercises at the end of each section make this an outstanding text for graduate and senior undergraduate students.

Author 
K. A. Stroud 
ISBN10 
0831131888 
Year 
2008 
Pages 
259 
Language 
en 
Publisher 
Industrial Press Inc. 
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Using the same innovative and proven approach that made the authors' Engineering Mathematics a worldwide bestseller, this book can be used in the classroom or as an indepth selfstudy guide. Its unique programmed approach patiently presents the mathematics in a stepbystep fashion together with a wealth of worked examples and exercises. It also contains Quizzes, Learning Outcomes, and Can You? checklists that guide readers through each topic and reinforce learning and comprehension. Both students and professionals alike will find this book a very effective learning tool and reference. Uses a unique programmed approach that takes readers through the mathematics in a stepbystep fashion with a wealth of worked examples and exercises. Contains many Quizzes, Learning Outcomes, and Can You? checklists. Ideal as a classroom textbook or a selflearning manual.

Author 
Derek J S Robinson 
ISBN10 
9789814365444 
Year 
20060815 
Pages 
372 
Language 
en 
Publisher 
World Scientific 
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This is the second edition of the bestselling introduction to linear algebra. Presupposing no knowledge beyond calculus, it provides a thorough treatment of all the basic concepts, such as vector space, linear transformation and inner product. The concept of a quotient space is introduced and related to solutions of linear system of equations, and a simplified treatment of Jordan normal form is given. Numerous applications of linear algebra are described, including systems of linear recurrence relations, systems of linear differential equations, Markov processes, and the Method of Least Squares. An entirely new chapter on linear programing introduces the reader to the simplex algorithm with emphasis on understanding the theory behind it. The book is addressed to students who wish to learn linear algebra, as well as to professionals who need to use the methods of the subject in their own fields.

Author 
Peter D. Lax 
ISBN10 
9781118626924 
Year 
20130520 
Pages 
392 
Language 
en 
Publisher 
John Wiley & Sons 
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Praise for the First Edition ". . .recommended for the teacher and researcher as well as for graduate students. In fact, [it] has a place on every mathematician's bookshelf." American Mathematical Monthly Linear Algebra and Its Applications, Second Edition presents linear algebra as the theory and practice of linear spaces and linear maps with a unique focus on the analytical aspects as well as the numerous applications of the subject. In addition to thorough coverage of linear equations, matrices, vector spaces, game theory, and numerical analysis, the Second Edition features studentfriendly additions that enhance the book's accessibility, including expanded topical coverage in the early chapters, additional exercises, and solutions to selected problems. Beginning chapters are devoted to the abstract structure of finite dimensional vector spaces, and subsequent chapters address convexity and the duality theorem as well as describe the basics of normed linear spaces and linear maps between normed spaces. Further updates and revisions have been included to reflect the most uptodate coverage of the topic, including: The QR algorithm for finding the eigenvalues of a selfadjoint matrix The Householder algorithm for turning selfadjoint matrices into tridiagonal form The compactness of the unit ball as a criterion of finite dimensionality of a normed linear space Additionally, eight new appendices have been added and cover topics such as: the Fast Fourier Transform; the spectral radius theorem; the Lorentz group; the compactness criterion for finite dimensionality; the characterization of commentators; proof of Liapunov's stability criterion; the construction of the Jordan Canonical form of matrices; and Carl Pearcy's elegant proof of Halmos' conjecture about the numerical range of matrices. Clear, concise, and superbly organized, Linear Algebra and Its Applications, Second Edition serves as an excellent text for advanced undergraduate and graduatelevel courses in linear algebra. Its comprehensive treatment of the subject also makes it an ideal reference or selfstudy for industry professionals.

Author 
Irving Kaplansky 
ISBN10 
0486432335 
Year 
1974 
Pages 
143 
Language 
en 
Publisher 
Courier Corporation 
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The author of this text seeks to remedy a common failing in teaching algebra: the neglect of related instruction in geometry. Focusing on inner product spaces, orthogonal similarity, and elements of geometry, this volume is illustrated with an abundance of examples, exercises, and proofs and is suitable for both undergraduate and graduate courses. 1974 edition.

Author 
Klaus Jänich 
ISBN10 
0387941282 
Year 
19940902 
Pages 
204 
Language 
en 
Publisher 
Springer Science & Business Media 
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The original version of this book, handed out to my students in weekly in stallments, had a certain rugged charm. Now that it is dressed up as a Springer UTM volume, I feel very much like Alfred Dolittle at Eliza's wedding. I hope the reader will still sense the presence of a young lecturer, enthusiastically urging his audience to enjoy linear algebra. The book is structured in various ways. For example, you will find a test in each chapter; you may consider the material up to the test as basic and the material following the test as supplemental. In principle, it should be possible to go from the test directly to the basic material of the next chapter. Since I had a mixed audience of mathematics and physics students, I tried to give each group some special attention, which in the book results in certain sections being marked· "for physicists" or "for mathematicians. " Another structural feature of the text is its division into laconic main text, put in boxes, and more talkative unboxed side text. If you follow just the main text, jumping from box to box, you will find that it makes coherent reading, a real "book within the book," presenting all that I want to teach.

Author 
Steven Roman 
ISBN10 
9780387728315 
Year 
20070920 
Pages 
526 
Language 
en 
Publisher 
Springer Science & Business Media 
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This graduate level textbook covers an especially broad range of topics. The book first offers a careful discussion of the basics of linear algebra. It then proceeds to a discussion of modules, emphasizing a comparison with vector spaces, and presents a thorough discussion of inner product spaces, eigenvalues, eigenvectors, and finite dimensional spectral theory, culminating in the finite dimensional spectral theorem for normal operators. The new edition has been revised and contains a chapter on the QR decomposition, singular values and pseudoinverses, and a chapter on convexity, separation and positive solutions to linear systems.

Author 
Gareth Williams 
ISBN10 
9781449679545 
Year 
20120901 
Pages 
589 
Language 
en 
Publisher 
Jones & Bartlett Publishers 
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Updated and revised to increase clarity and further improve student learning, the Eighth Edition of Gareth Williams' classic text is designed for the introductory course in linear algebra. It provides a flexible blend of theory and engaging applications for students within engineering, science, mathematics, business management, and physics. It is organized into three parts that contain core and optional sections. There is then ample time for the instructor to select the material that gives the course the desired flavor. Part 1 introduces the basics, presenting systems of linear equations, vectors and subspaces of Rn, matrices, linear transformations, determinants, and eigenvectors. Part 2 builds on the material presented in Part1 and goes on to introduce the concepts of general vector spaces, discussing properties of bases, developing the rank/nullity theorem, and introducing spaces of matrices and functions. Part 3 completes the course with important ideas and methods of numerical linear algebra, such as illconditioning, pivoting, and LU decomposition. Throughout the text the author takes care to fully and clearly develop the mathematical concepts and provide modern applications to reinforce those concepts. The applications range from theoretical applications within differential equations and least square analysis, to practical applications in fields such as archeology, demography, electrical engineering and more. New exercises can be found throughout that tie back to the modern examples in the text. Key Features of the Eighth Edition: • Updated and revised throughout with new section material and exercises. • Each section begins with a motivating introduction, which ties material to the previously learned topics. • Carefully explained examples illustrate key concepts throughout the text. • Includes such new topics such as QR Factorization and Singular Value Decomposition. • Includes new applications such as a Leslie Matrix model that is used to predict birth and death patterns of animals. • Includes discussions of the role of linear algebra in many areas, such as the operation of the search engine Google and the global structure of the worldwide air transportation network. • A MATLAB manual that ties into the regular course material is included as an appendix. These ideas can be implemented on any matrix algebra software package. This manual consists of 28 sections that tie into the regular course material. • Graphing Calculator Manual included as an appendix. • A Student Solutions Manual that contains solutions to selected exercises is available as a supplement. An Instructors Complete Solutions Manual, test bank, and PowerPoint Lecture Outlines are also available. • Available with WebAssign Online Homework & Assessment