Basic Linear Algebra

Basic Linear Algebra PDF Author: Thomas S. Blyth
Publisher: Springer Science & Business Media
ISBN: 1447134966
Category : Mathematics
Languages : en
Pages : 211

Book Description
Basic Linear Algebra is a text for first year students, working from concrete examples towards abstract theorems, via tutorial-type exercises. The book explains the algebra of matrices with applications to analytic geometry, systems of linear equations, difference equations, and complex numbers. Linear equations are treated via Hermite normal forms, which provides a successful and concrete explanation of the notion of linear independence. Another highlight is the connection between linear mappings and matrices, leading to the change of basis theorem which opens the door to the notion of similarity. The authors are well known algebraists with considerable experience of teaching introductory courses on linear algebra to students at St Andrews. This book is based on one previously published by Chapman and Hall, but it has been extensively updated to include further explanatory text and fully worked solutions to the exercises that all 1st year students should be able to answer.

Basic Linear Algebra

Basic Linear Algebra PDF Author: T.S. Blyth
Publisher: Springer Science & Business Media
ISBN: 1447106814
Category : Mathematics
Languages : en
Pages : 242

Book Description
Basic Linear Algebra is a text for first year students leading from concrete examples to abstract theorems, via tutorial-type exercises. More exercises (of the kind a student may expect in examination papers) are grouped at the end of each section. The book covers the most important basics of any first course on linear algebra, explaining the algebra of matrices with applications to analytic geometry, systems of linear equations, difference equations and complex numbers. Linear equations are treated via Hermite normal forms which provides a successful and concrete explanation of the notion of linear independence. Another important highlight is the connection between linear mappings and matrices leading to the change of basis theorem which opens the door to the notion of similarity. This new and revised edition features additional exercises and coverage of Cramer's rule (omitted from the first edition). However, it is the new, extra chapter on computer assistance that will be of particular interest to readers: this will take the form of a tutorial on the use of the "LinearAlgebra" package in MAPLE 7 and will deal with all the aspects of linear algebra developed within the book.

Basic Linear Algebra

Basic Linear Algebra PDF Author: Thomas S. Blyth
Publisher:
ISBN: 9781447134978
Category :
Languages : en
Pages : 216

Book Description

A First Course in Linear Algebra

A First Course in Linear Algebra PDF Author: A. G. Hamilton
Publisher: CUP Archive
ISBN: 9780521310413
Category : Mathematics
Languages : en
Pages : 164

Book Description
This is a short, readable introduction to basic linear algebra, as usually encountered in a first course. The development of the subject is integrated with a large number of worked examples that illustrate the ideas and methods. The format of the book, with text and relevant examples on facing pages means that the reader can follow the text uninterrupted. The student should be able to work through the book and learn from it sequentially. Stress is placed on applications of the methods rather than on developing a logical system of theorems. Numerous exercises are provided.

A First Course in Linear Algebra

A First Course in Linear Algebra PDF Author: Minking Eie
Publisher: World Scientific Publishing Company
ISBN: 9813143134
Category : Mathematics
Languages : en
Pages : 388

Book Description
A First Course in Linear Algebra is written by two experts from algebra who have more than 20 years of experience in algebra, linear algebra and number theory. It prepares students with no background in Linear Algebra. Students, after mastering the materials in this textbook, can already understand any Linear Algebra used in more advanced books and research papers in Mathematics or in other scientific disciplines. This book provides a solid foundation for the theory dealing with finite dimensional vector spaces. It explains in details the relation between linear transformations and matrices. One may thus use different viewpoints to manipulate a matrix instead of a one-sided approach. Although most of the examples are for real and complex matrices, a vector space over a general field is briefly discussed. Several optional sections are devoted to applications to demonstrate the power of Linear Algebra.

Linear Algebra

Linear Algebra PDF Author: H. E. Rose
Publisher: Springer Science & Business Media
ISBN: 9783764369057
Category : Mathematics
Languages : en
Pages : 276

Book Description
Linear algebra is one of the most important branches of mathematics - important because of its many applications to other areas of mathematics, and important because it contains a wealth of ideas and results which are basic to pure mathematics. This book gives an introduction to linear algebra, and develops and proves its fundamental properties and theorems taking a pure mathematical approach - linear algebra contains some fine pure mathematics. Main topics: - vector spaces and algebras, dimension, linear maps, direct sums, and (briefly) exact sequences - matrices and their connections with linear maps, determinants (properties proved using some elementary group theory), and linear equations - Cayley-Hamilton and Jordan theorems leading to the spectrum of a linear map - this provides a geometric-type description of these maps - Hermitian and inner product spaces introducing some metric properties (distance, perpendicularity etc.) into the theory, also unitary and orthogonal maps and matrices - applications to finite fields, mathematical coding theory, finite matrix groups, the geometry of quadratic forms, quaternions and Cayley numbers, and some basic group representation theory A large number of examples, exercises and problems are provided. Answers and/or sketch solutions to all of the problems are given in an appendix. Some of these are theoretical and some numerical, both types are important. No particular computer algebra package is discussed but a number of the exercises are intended to be solved using one of these packages chosen by the reader.The approach is pure-mathematical, and the intended readership is undergraduate mathematicians, also anyone who requires a more than basic understanding of the subject. This book will be most useful for a "second course" in linear algebra, that is for students that have seen some elementary matrix algebra. But as all terms are defined from scratch, the book can be used for a "first course" for more advanced students.

Linear Algebra in Action

Linear Algebra in Action PDF Author: Harry Dym
Publisher: American Mathematical Soc.
ISBN: 1470409089
Category : Mathematics
Languages : en
Pages : 585

Book Description
Linear algebra permeates mathematics, perhaps more so than any other single subject. It plays an essential role in pure and applied mathematics, statistics, computer science, and many aspects of physics and engineering. This book conveys in a user-friendly way the basic and advanced techniques of linear algebra from the point of view of a working analyst. The techniques are illustrated by a wide sample of applications and examples that are chosen to highlight the tools of the trade. In short, this is material that many of us wish we had been taught as graduate students. 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.

Further Linear Algebra

Further Linear Algebra PDF Author: T.S. Blyth
Publisher: Springer Science & Business Media
ISBN: 144710661X
Category : Mathematics
Languages : en
Pages : 239

Book Description
Most of the introductory courses on linear algebra develop the basic theory of finite dimensional vector spaces, and in so doing relate the notion of a linear mapping to that of a matrix. Generally speaking, such courses culminate in the diagonalisation of certain matrices and the application of this process to various situations. Such is the case, for example, in our previous SUMS volume Basic Linear Algebra. The present text is a continuation of that volume, and has the objective of introducing the reader to more advanced properties of vector spaces and linear mappings, and consequently of matrices. For readers who are not familiar with the contents of Basic Linear Algebra we provide an introductory chapter that consists of a compact summary of the prerequisites for the present volume. In order to consolidate the student's understanding we have included a large num ber of illustrative and worked examples, as well as many exercises that are strategi cally placed throughout the text. Solutions to the exercises are also provided. Many applications of linear algebra require careful, and at times rather tedious, calculations by hand. Very often these are subject to error, so the assistance of a com puter is welcome. As far as computation in algebra is concerned, there are several packages available. Here we include, in the spirit of a tutorial, a chapter that gives 1 a brief introduction to the use of MAPLE in dealing with numerical and algebraic problems in linear algebra.

Basic Linear Algebra

Basic Linear Algebra PDF Author: Gregor Olsavsky
Publisher:
ISBN: 9780595406449
Category : Mathematics
Languages : en
Pages : 366

Book Description
This book is an introductory linear algebra text. The topics are covered in the traditional order: linear systems, matrix algebra, vector spaces, linear transformations, orthogonality, and the eigenvalue/eigenvector problem. The book seeks to explain and discover the important concepts of linear algebra using well-chosen examples. Proofs of many important results are done if the proof can be accomplished in a succinct, straightforward fashion. There are over 100 worked-out examples in the text as well as a complete outline of every chapter and extensive review problems which test the students knowledge of the material covered in each chapter. There are over 1200 exercises in the text, which were created by the author with care to include exercises which resemble problems done in the text. Definitions are well marked and theorems are stated as briefly as possible in order to enhance the ability of the student to remember the result. In a slightly novel way, the answers to the odd problems are given directly next to the problem. Applications such as heat transfer, spring/mass systems, population dynamics, and systems of differential equations are sprinkled throughout the text.

Linear Algebra

Linear Algebra PDF Author: Edgar G Goodaire
Publisher: World Scientific Publishing Company
ISBN: 981450839X
Category : Mathematics
Languages : en
Pages : 732

Book Description
This is a matrix-oriented approach to linear algebra that covers the traditional material of the courses generally known as “Linear Algebra I” and “Linear Algebra II” throughout North America, but it also includes more advanced topics such as the pseudoinverse and the singular value decomposition that make it appropriate for a more advanced course as well. As is becoming increasingly the norm, the book begins with the geometry of Euclidean 3-space so that important concepts like linear combination, linear independence and span can be introduced early and in a “real” context. The book reflects the author's background as a pure mathematician — all the major definitions and theorems of basic linear algebra are covered rigorously — but the restriction of vector spaces to Euclidean n-space and linear transformations to matrices, for the most part, and the continual emphasis on the system Ax=b, make the book less abstract and more attractive to the students of today than some others. As the subtitle suggests, however, applications play an important role too. Coding theory and least squares are recurring themes. Other applications include electric circuits, Markov chains, quadratic forms and conic sections, facial recognition and computer graphics.
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