Text covers sets and mappings, vector spaces, matrices, linear functionals, other basics; plus linear programming, Tchebychev approximations, more. Ideal introduction for undergraduates; reference for theoretical, applied mathematicians. Problems and exercises.
Rigorous, self-contained coverage of determinants, vectors, matrices and linear equations, quadratic forms, more. Elementary, easily readable account with numerous examples and problems at the end of each chapter.
Ward Cheney and David Kincaid have developed Linear Algebra: Theory and Applications, Second Edition, a multi-faceted introductory textbook, which was motivated by their desire for a single text that meets the various requirements for differing courses within linear algebra. For theoretically-oriented students, the text guides them as they devise proofs and deal with abstractions by focusing on a comprehensive blend between theory and applications. For application-oriented science and engineering students, it contains numerous exercises that help them focus on understanding and learning not only vector spaces, matrices, and linear transformations, but uses of software tools available for use in applied linear algebra. Using a flexible design, it is an ideal textbook for instructors who wish to make their own choice regarding what material to emphasis, and to accentuate those choices with homework assignments from a large variety of exercises, both in the text and online.
Rigorous, self-contained introduction at undergraduate level covers vector spaces and linear transformations, linear equations and determinants, characteristic roots. Includes 16 sets of true-false quizzes and exercises — with worked-out solutions — a complete theory of permutations and much more.
As the basis of equations (and therefore problem-solving), linear algebra is the most widely taught sub-division of pure mathematics. Dr Allenby has used his experience of teaching linear algebra to write a lively book on the subject that includes historical information about the founders of the subject as well as giving a basic introduction to the mathematics undergraduate. The whole text has been written in a connected way with ideas introduced as they occur naturally. As with the other books in the series, there are many worked examples.
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, Euclidean spaces, unitary spaces, quadratic forms in Euclidean and unitary spaces, finite-dimensional space. Problems with hints and answers.
Basic textbook covers theory of matrices and its applications to systems of linear equations and related topics such as determinants, eigenvalues, and differential equations. Includes numerous exercises.
"Linear Algebra" is intended for a one-term 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 finite-dimensional Krein-Milman 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 self-contained. In this new edition, many parts of the book have been rewritten and reorganized, and new exercises have been added.
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 student–friendly 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 up–to–date coverage of the topic, including: The QR algorithm for finding the eigenvalues of a self–adjoint matrix The Householder algorithm for turning self–adjoint 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 graduate–level courses in linear algebra. Its comprehensive treatment of the subject also makes it an ideal reference or self–study for industry professionals.
This book provides a rigorous introduction to the basic aspects of the theory of linear estimation and hypothesis testing, covering the necessary prerequisites in matrices, multivariate normal distribution and distributions of quadratic forms along the way. It will appeal to advanced undergraduate and first-year graduate students, research mathematicians and statisticians.
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 non-negative operators, isometries, and polar and singular-value 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.
Useful Concepts and Results at the Heart of Linear Algebra A one- or two-semester course for a wide variety of students at the sophomore/junior undergraduate level A Modern Introduction to Linear Algebra provides a rigorous yet accessible matrix-oriented introduction to the essential concepts of linear algebra. Concrete, easy-to-understand examples motivate the theory. The book first discusses vectors, Gaussian elimination, and reduced row echelon forms. It then offers a thorough introduction to matrix algebra, including defining the determinant naturally from the PA=LU factorization of a matrix. The author goes on to cover finite-dimensional real vector spaces, infinite-dimensional spaces, linear transformations, and complex vector spaces. The final chapter presents Hermitian and normal matrices as well as quadratic forms. Taking a computational, algebraic, and geometric approach to the subject, this book provides the foundation for later courses in higher mathematics. It also shows how linear algebra can be used in various areas of application. Although written in a "pencil and paper" manner, the text offers ample opportunities to enhance learning with calculators or computer usage. Solutions manual available for qualifying instructors
This book discusses fundamental ideas of linear algebra. The author presents the spectral theory of nonselfadjoint matrix operators and matrix pencils in a finite dimensional Euclidean space. Statements of computational problems and brief descriptions of numerical algorithms, some of them nontraditional, are given. Proved in detail are classical problems that are not usually found in standard university courses. In particular, the material shows the role of delicate estimates for the resolvent of an operator and underscores the need for the study and use of such estimates in numerical analysis.
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.
This book introduces the concepts of linear algebra through the careful study of two and three-dimensional Euclidean geometry. This approach makes it possible to start with vectors, linear transformations, and matrices in the context of familiar plane geometry and to move directly to topics such as dot products, determinants, eigenvalues, and quadratic forms. The later chapters deal with n-dimensional Euclidean space and other finite-dimensional vector space.
This solutions manual for Lang’s Undergraduate Analysis provides worked-out solutions for all problems in the text. They include enough detail so that a student can fill in the intervening details between any pair of steps.
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 the author wishes he had been taught as a graduate student. 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. The book is suitable as a text or supplementary reference for a variety of courses on linear algebra and its applications, as well as for self-study.