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.
Linear Algebra constitutes a foundation course for those specializing in the fields of mathematics, engineering and science. The course normally takes one semester, but for those needing a more rigorous study of the subject, it involve up to two semesters.This book is based on the lecture notes given for the linear algebra course at the Department of Mathematics in Wuhan University.
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.
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.
Emphasis is placed on applications in preference to more theoretical aspects throughout this readable introduction to linear algebra for specialists as well as non-specialists. An expanded version of A First Course in Linear Algebra.
"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.
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 in-depth self-study guide. Its unique programmed approach patiently presents the mathematics in a step-by-step 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 step-by-step 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 self-learning manual.
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 ...
David Poole's innovative LINEAR ALGEBRA: A MODERN INTRODUCTION, 4e emphasizes a vectors approach and better prepares students to make the transition from computational to theoretical mathematics. Balancing theory and applications, the book is written in a conversational style and combines a traditional presentation with a focus on student-centered learning. Theoretical, computational, and applied topics are presented in a flexible yet integrated way. Stressing geometric understanding before computational techniques, vectors and vector geometry are introduced early to help students visualize concepts and develop mathematical maturity for abstract thinking. Additionally, the book includes ample applications drawn from a variety of disciplines, which reinforce the fact that linear algebra is a valuable tool for modeling real-life problems. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version.
This popular and successful text was originally written for a one-semester 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.