Top Marketplace offers for ISBN
# 9780130084514

Not the book you're looking for? Search for all books with this author and title

** ** This top-selling, theorem-proof book presents a careful treatment of the principle topics of linear algebra, and illustrates the power of the subject through a variety of applications. It emphasizes the symbiotic relationship between linear transformations and matrices, but states theorems in the more general infinite-dimensional case where appropriate. ** ** Chapter topics cover vector spaces, linear transformations and matrices, elementary matrix operations and systems of linear equations, determinants, diagonalization, inner product spaces, and canonical forms. ** ** For statisticians and engineers.

*"synopsis" may belong to another edition of this title.*

The language and concepts of matrix theory and, more generally, of linear algebra have come into widespread usage in the social and natural sciences, computer science, and statistics. 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 6.1 through 6.5. 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 eve prove 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 1.4.

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 4.1 through 4.3) and a summary of important facts that are needed for the remaining chapters (Section 4.4). Optional Section 4.5 presents an axiomatic development of the determinant.

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 5.4 contains material on invariant subspaces and the Cayley-Hamilton theorem.

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 6.1 through 6.6. Sections 6.7 through 6.11 contain diverse applications of the rich inner product space structure.

Canonical forms are treated in Chapter 7. Sections 7.1 and 7.2 develop the Jordan canonical form, Section 7.3 presents the minimal polynomial, and Section 7.4 discusses the rational canonical form.

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 7.4. We prefer to cite particular results from the appendices as needed rather than to discuss the appendices independently.

**DIFFERENCES BETWEEN THE THIRD AND FOURTH EDITIONS**

The principal content change of this fourth edition is the inclusion of a new section (Section 6.7) discussing the singular value decomposition and the pseudoinverse of a matrix or a linear transformation between finite-dimensional inner product spaces. Our approach is to treat this material as a generalization of our characterization of normal and self-adjoint operators.

The organization of the text is essentially the same as in the third edition. Nevertheless, this edition contains many significant local changes that improve the book. Section 5.1 (Eigenvalues and Eigenvectors) has been streamlined, and some material previously in Section 5.1 has been moved to Section 2.5 (The Change of Coordinate Matrix). Further improvements include revised proofs of some theorems, additional examples, new exercises, and literally hundreds of minor editorial changes.

We are especially indebted to Jane M. Day (San Jose State University) for her extensive and detailed comments on the fourth edition manuscript. Additional comments were provided by the following reviewers of the fourth edition manuscript: Thomas Banchoff (Brown University), Christopher Heil (Georgia Institute of Technology), and Thomas Shemanske (Dartmouth College).

*"About this title" may belong to another edition of this title.*

ISBN 10: 0130084514
ISBN 13: 9780130084514

New
Quantity Available: 10

Seller

Rating

**Book Description **Book Condition: New. Brand new book. This is an international edition textbook with identical content as the US version. We ship all our orders from CA/IL, USA (depending on your address) and NOT from Asia! Choose expedited shipping for superfast delivery with tracking. Bookseller Inventory # 9780130084514

More Information About This Seller | Ask Bookseller a Question

ISBN 10: 0130084514
ISBN 13: 9780130084514

New
Softcover
Quantity Available: 2

Seller

Rating

**Book Description **Softcover. Book Condition: New. International Edition, Brand NEW, Shrink Wrapped, Paperback, Ships from US Warehouse with tracking number. Choose Expedited Shipping for GUARANTEED **5 DAY DELIVERY**. ISBN and Cover page may differ. International edition does not comes with CD/access code. Book cover may contain restrictions but it is absolutely legal to use, may be printed in black & white having similar contents as US edition. Best Customer Support. ****Please Read Description Carefully Before Buying. Occasionally, international textbooks may come with different exercises at the end of chapters. Bookseller Inventory # US_9780130084514

More Information About This Seller | Ask Bookseller a Question

Published by
Pearson

ISBN 10: 0130084514
ISBN 13: 9780130084514

New
Softcover
Quantity Available: > 20

Seller

Rating

**Book Description **Pearson. Book Condition: New. 0130084514 International Edition, Brand New, Paperback Delivery within 6-14 business days, Similar Contents as U.S Edition, ISBN and Cover design may differ, printed in Black & White. Choose Expedited shipping for delivery within 4-7 business days.We do not ship to PO Box, APO , FPO Address. In some instances, subjects such as Management, Accounting, Finance may have different end chapter case studies and exercises. International Edition Textbooks may bear a label "Not for sale in the U.S. or Canada" and "Content may different from U.S. Edition" - printed only to discourage U.S. students from obtaining an affordable copy. The U.S. Supreme Court has asserted your right to purchase international editions, and ruled on this issue. Access code/CD is not provided with these editions , unless specified.We may ship the books from multiple warehouses across the globe, including India depending upon the availability of inventory storage. Customer satisfaction guaranteed. Bookseller Inventory # UM14_9780130084514

More Information About This Seller | Ask Bookseller a Question

ISBN 10: 0130084514
ISBN 13: 9780130084514

New
Softcover
Quantity Available: 20

Seller

Rating

**Book Description **Book Condition: New. International Edition Brand New Paperback Same Title Author and Edition as listed. ISBN and Cover design differs. Similar Contents as U.S Edition. Standard Delivery within 6-14 business days ACROSS THE GLOBE. We can ship to PO Box address in US. International Edition Textbooks may bear a label "Not for sale in the U.S. or Canada" or "For sale in Asia only" or similar restrictions- printed only to discourage students from obtaining an affordable copy. US Court has asserted your right to buy and use International edition. Access code/CD may not provided with these editions. We may ship the books from multiple warehouses across the globe including Asia depending upon the availability of inventory. Printed in English. Customer satisfaction guaranteed. Bookseller Inventory # HU14_9780130084514

More Information About This Seller | Ask Bookseller a Question

ISBN 10: 0130084514
ISBN 13: 9780130084514

New
Soft cover
Quantity Available: > 20

Seller

Rating

**Book Description **Soft cover. Book Condition: New. 4th Edition, International Edition. Brand New, SoftcoverBlack & White or color International Edition. GET IT FAST within 3-5 business days by UPS/DHL worldwide express with Tracking Number. Book printed in English. No shipping to PO Box/APO/FPO address. The international edition will has different ISBN and Cover design fromUSedition.[Please Read Carefully Before Buying]Occasionally, international textbooks may come with different exercises at the end of chapters. Restricted sales disclaimer wordings |Not for Sales inUSAand Canada| are printed on the cover of the book only to misguide the students to prevent them from the purchasing the books. But in recent proceedings of court ruled that it is legal to buy/sell international edition inNorth America. We may ship the books fromIndiaor other Asian regions for inventory purpose. Return policy only for 30 days. Customer satisfaction guaranteed and in case of any queries please email us. Bookseller Inventory # GBD127439

More Information About This Seller | Ask Bookseller a Question

ISBN 10: 0130084514
ISBN 13: 9780130084514

New
Soft cover
Quantity Available: > 20

Seller

Rating

**Book Description **Soft cover. Book Condition: New. FAST 2 to 3 day Expedited Shipment - Brand NEW - International Edition - 4ed - SAME Contents as in US edition - SHRINKwrapped BOXpacked - Legal to use in USA for personal use. Bookseller Inventory # A40

More Information About This Seller | Ask Bookseller a Question

ISBN 10: 0130084514
ISBN 13: 9780130084514

New
Quantity Available: 1

Seller

Rating

**Book Description **Book Condition: Brand New. Brand New International Edition, Perfect Condition. Printed in English. Excellent Quality, Service and customer satisfaction guaranteed!. Bookseller Inventory # USAND-45897

More Information About This Seller | Ask Bookseller a Question

ISBN 10: 0130084514
ISBN 13: 9780130084514

New
Quantity Available: 20

Seller

Rating

**Book Description **Book Condition: New. New. Soft Cover International edition. Different ISBN and Cover image but contents are same as US edition.Perfect condition. Ship by express service to USA, Canada, Australia, France, Italy, UK, Germany and Netherland. Customer satisfaction our priority. Bookseller Inventory # ABE-190516-110931

More Information About This Seller | Ask Bookseller a Question

ISBN 10: 0130084514
ISBN 13: 9780130084514

New
Quantity Available: 20

Seller

Rating

**Book Description **Book Condition: Brand New. New. Soft Cover International edition. Different ISBN and Cover image but contents are same as US edition. Customer Satisfaction guaranteed!!. Bookseller Inventory # SHAK110931

More Information About This Seller | Ask Bookseller a Question

ISBN 10: 0130084514
ISBN 13: 9780130084514

New
Quantity Available: 5

Seller

Rating

**Book Description **Book Condition: Brand New. Brand New International Edition, Perfect Condition. Printed in English. Excellent Quality, Service and customer satisfaction guaranteed!. Bookseller Inventory # USAND-108467

More Information About This Seller | Ask Bookseller a Question