Spence cover the following topics. Vector Spaces 2. Linear Transformations and Matrices 3. Elementary Matrix Operations and Systems of Linear Equations 4. Determinants 5. Diagonalization 6. Inner Product Spaces 7. Canonical Forms Appendices A: Sets Appendices B: Functions Appendices C: Fields Appendices D: Complex Numbers Appendices E: Polynomials Answers to Selected Exercises. Open or Download Similar Books. We provide it which is already avialable on the internet. For any further querries please contact us. We never SUPPORT PIRACY. This copy was provided for students who are financially troubled but want studeing to learn.

Thank you. About Us Math shortcuts, Articles, worksheets, Exam tips, Question, Answers, FSc, BSc, MSc More about us. Login to Your Account. Remember me. Home Question Order of operation BODMAS Exponent Numbering System Undefined, Indeterminate Differentiation Integration Why "e" is important in math. Insel , Lawrence E. Spense PDF Add to Wishlist Share. This document was uploaded by our user. The uploader already confirmed that they had the permission to publish it. Report DMCA. E-Book Overview Illustrates the power of linear algebra through practical applications This acclaimed theorem-proof text presents a careful treatment of the principal topics of linear algebra.

It emphasizes the symbiotic relationship between linear transformations and matrices, but states theorems in the more general infinite-dimensional case where appropriate. E-Book Information Year: 2, Edition: 5 City: Upper Saddle River, New Jersey Pages: Pages In File: Language: English Identifier: , Org File Size: 69,, Extension: pdf Toc: Linear Algebra Contents Preface To the Student 1 Vector Spaces 2 Linear Transformations and Matrices 3 Elementary Matrix Operations and Systems of Linear Equations 4 Determinants 5 Diagonalization 6 Inner Product Spaces 7 Canonical Forms Appendices Index.

Pages Page size DOWNLOAD FILE. Graduate Texts in Mathematics Linear Algebra Volume 23 Springer Graduate Texts in Mathematics 23 Editorial Bo. Linear Algebra This page intentionally left blank Fourth Edition Stephen H. Friedberg Arnold J. Insel Lawrence E. Spence Illinois State University PEARSON EDUCATION, Upper Saddle River, New Jersey Library of Congress Cataloging-in-Publication Data Friedberg, Stephen H. Friedberg, Arnold J. Insel, Lawrence E. Includes indexes. ISBN 1. Algebra, Linear. Insel, Arnold J. Spence, Lawrence E. Dreifachgewebe: Baumwolle und Kunstseide, schwarz, weiß, Orange × cm. Foto: Gunter Lepkowski, Berlin. Bauhaus-Archiv, Berlin, Inv. c , , , by Pearson Education, Inc. Upper Saddle River, New Jersey All rights reserved. No part of this book may be reproduced, in any form or by any means, without permission in writing from the publisher.

Printed in the United States of America 10 9 8 7 6 5 4 3 2 1 ISBN Pearson Pearson Pearson Pearson Pearson Pearson Pearson Pearson Education, Ltd. Limited, Sydney Education Singapore, Pte. Education -- Japan, Tokyo Education Malaysia, Pte. Ltd To our families: Ruth Ann, Rachel, Jessica, and Jeremy Barbara, Thomas, and Sara Linda, Stephen, and Alison This page intentionally left blank Contents Preface ix 1 Vector Spaces 1 1. Vector Spaces. Linear Combinations and Systems of Linear Equations. Linear Dependence and Linear Independence. Bases and Dimension. Maximal Linearly Independent Subsets. Index of Definitions. The Matrix Representation of a Linear Transformation Composition of Linear Transformations and Matrix Multiplication. Invertibility and Isomorphisms. The Change of Coordinate Matrix. Dual Spaces. Homogeneous Linear Differential Equations with Constant Coefficients. v vi Table of Contents 3. Systems of Linear Equations—Theoretical Aspects.

Systems of Linear Equations—Computational Aspects Index of Definitions. Determinants of Order n. Properties of Determinants. Summary—Important Facts about Determinants A Characterization of the Determinant. Matrix Limits and Markov Chains. Invariant Subspaces and the Cayley—Hamilton Theorem Index of Definitions. The Gram—Schmidt Orthogonalization Process and Orthogonal Complements. Table of Contents vii 7 Canonical Forms 7. The Jordan Canonical Form II The Minimal Polynomial. The Rational Canonical Form. Appendices A B C D E Sets. Complex Numbers Polynomials. Answers to Selected Exercises. In addition, linear algebra continues to be of great importance in modern treatments of geometry and analysis.

The primary purpose of this fourth edition of Linear Algebra is to present a careful treatment of the principal topics of linear algebra and to illustrate the power of the subject through a variety of applications. Our major thrust emphasizes the symbiotic relationship between linear transformations and matrices. However, where appropriate, theorems are stated in the more general infinite-dimensional case. For example, this theory is applied to finding solutions to a homogeneous linear differential equation and the best approximation by a trigonometric polynomial to a continuous function. Although the only formal prerequisite for this book is a one-year course in calculus, it requires the mathematical sophistication of typical junior and senior mathematics majors. This book is especially suited for a second course in linear algebra that emphasizes abstract vector spaces, although it can be used in a first course with a strong theoretical emphasis.

The book is organized to permit a number of different courses ranging from three to eight semester hours in length to be taught from it. The core material vector spaces, linear transformations and matrices, systems of linear equations, determinants, diagonalization, and inner product spaces is found in Chapters 1 through 5 and Sections 6. Chapters 6 and 7, on inner product spaces and canonical forms, are completely independent and may be studied in either order. In addition, throughout the book are applications to such areas as differential equations, economics, geometry, and physics. These applications are not central to the mathematical development, however, and may be excluded at the discretion of the instructor. We have attempted to make it possible for many of the important topics of linear algebra to be covered in a one-semester course.

This goal has led us to develop the major topics with fewer preliminaries than in a traditional approach. Our treatment of the Jordan canonical form, for instance, does not require any theory of polynomials. The resulting economy permits us to cover the core material of the book omitting many of the optional sections and a detailed discussion of determinants in a one-semester four-hour course for students who have had some prior exposure to linear algebra. Chapter 1 of the book presents the basic theory of vector spaces: subspaces, linear combinations, linear dependence and independence, bases, and dimension. The chapter concludes with an optional section in which we prove ix x Preface that every infinite-dimensional vector space has a basis.

Linear transformations and their relationship to matrices are the subject of Chapter 2. We discuss the null space and range of a linear transformation, matrix representations of a linear transformation, isomorphisms, and change of coordinates. Optional sections on dual spaces and homogeneous linear differential equations end the chapter. The application of vector space theory and linear transformations to systems of linear equations is found in Chapter 3. We have chosen to defer this important subject so that it can be presented as a consequence of the preceding material. This approach allows the familiar topic of linear systems to illuminate the abstract theory and permits us to avoid messy matrix computations in the presentation of Chapters 1 and 2.

There are occasional examples in these chapters, however, where we solve systems of linear equations. Of course, these examples are not a part of the theoretical development. The necessary background is contained in Section 1. Determinants, the subject of Chapter 4, are of much less importance than they once were. In a short course less than one year , we prefer to treat determinants lightly so that more time may be devoted to the material in Chapters 5 through 7. Consequently we have presented two alternatives in Chapter 4—a complete development of the theory Sections 4. Optional Section 4. Chapter 5 discusses eigenvalues, eigenvectors, and diagonalization. One of the most important applications of this material occurs in computing matrix limits. We have therefore included an optional section on matrix limits and Markov chains in this chapter even though the most general statement of some of the results requires a knowledge of the Jordan canonical form.

Section 5. Inner product spaces are the subject of Chapter 6. The basic mathematical theory inner products; the Gram—Schmidt process; orthogonal complements; the adjoint of an operator; normal, self-adjoint, orthogonal and unitary operators; orthogonal projections; and the spectral theorem is contained in Sections 6. Sections 6. Canonical forms are treated in Chapter 7. Sections 7. There are five appendices. The first four, which discuss sets, functions, fields, and complex numbers, respectively, are intended to review basic ideas used throughout the book. Appendix E on polynomials is used primarily in Chapters 5 and 7, especially in Section 7. We prefer to cite particular results from the appendices as needed rather than to discuss the appendices Preface xi independently. The following diagram illustrates the dependencies among the various chapters. Chapter 1?

Chapter 2? Chapter 3? Sections 4.

We call LA a left-multiplication transformation. Prove that the upper triangular matrices form a subspace of Mm×n F. A basis for a vector space V is a linearly independent subset of V that generates V. If S2 is linearly independent, then S1 is linearly independent. E-Book Overview Illustrates the power of linear algebra through practical applications This acclaimed theorem-proof text presents a careful treatment of the principal topics of linear algebra.

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