Linear Algebra - Second Edition

Sep 14, 2026

Uploaded by Anda

Linear Algebra - Second Edition is an undergraduate-focused textbook designed to support a variety of linear algebra courses and teaching lengths. The revision expands flexibility for instructors by introducing natural stopping points and increasing coverage to support both one-year progression and reference use. Key updates emphasize canonical forms and inner product spaces, restructuring the treatment of characteristic values, triangulation, diagonalization, and subsequent development of sesquilinear forms and normal operators. The text balances conceptual understanding with extensive examples and graded exercises.

LanguageEnglish

CategoryExam

FormatPDF

Pages416

Reading Time17 h 28 min

AccessFree to download

Preface

Teaching scope and course flexibility

Major changes in canonical forms and inner product spaces

Approach to abstraction and learning supports

Examples and graded exercises

Chapter overview

LINEAR ALGEBRA Second Edition KENNETH HOFFMAN Professor of Mathematics Massachusetts Institute of Technology RAY KUNZE Professor of Mathematics University of California, Irvine PRENTICE-HALL, INC. , Englewood Cliffs, New Jersey © 1971, 1961 by Prentice-Hall, Inc. Englewood Cliffs, 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. PRENTICE-HALL INTERNATIONAL, INC., London PRENTICE-HALL OF AUSTRALIA, P'l'Y. W'D., Sydney PRENTICE-HALL OF CANADA, LTD., Toronto PRENTICE-HALL OF INDIA PRIVATE LIMITED, New Delhi PRENTICE-HALL OF JAPAN, INC., Tokyo Current printing (last digit): 10 9 8 7 6 Library of Congress Catalog Card No. 75-142120 Printed in the United States of America Preface Our original purpose in writing this book was to provide a text for the undergraduate linear algebra course at the Massachusetts Institute of Technology. This course was designed for mathematics majors at the junior level, although three fourths of the students were drawn from other scientific and technological disciplinesand ranged from freshmen through graduate students. This description of the M.LT. audience for the text remains generally accurate today. The ten years since the first edition have seen the proliferation of linear algebra courses throughout the country and have afforded one of the authors the opportunity to teach the basic material to a variety of groups at Brandeis University, Washington University (St. Louis) , and the University of California (Irvine) . Our principal aim in revising Linear Algebra has been to increase the variety of courses which can easily be taught from it. On one hand, we have structured the chapters, especially the more difficult ones, so that there are several natural stopping points along the way, allowing the instructor in a one-quarter or one-semester course to exercise a considerable amount of choice in the subject matter. On the other hand, we have increased the amount of material in the text, so that it can be used for a rather comprehensive one-year course in linear algebra and even as a reference book for mathematicians. The major changes have been in our treatments of canonical forms and inner product spaces. In Chapter 6 we no longer begin with the general spatial theory which underlies the theory of canonical forms. We first handle characteristic values in relation to triangulation and diagonalization theorems and then build our way up to the general theory. We have split Chapter 8 so that the basic material on inner product spaces and unitary diagonalization is followed by a Chapter 9 which treats sesqui-linear forms and the more sophisticated properties of normal operators, including normal operators on real inner product spaces. We have also made a number of small changes and improvements from the first edition. But the basic philosophy behind the text is unchanged. We have made no particular concession to the fact that the majority of the students may not be primarily interested in mathematics. For we believe a mathematics course should not give science, engineering, or social science students a hodgepodge of techniques, but should provide them with an understanding of basic mathematical concepts. iv Preface On the other hand, we have been keenly aware of the wide range of backgrounds which the students may possess and, in particular, of the fact that the students have had very little experience with abstract mathematical reasoning. For this reason, we have avoided the introduction of too many abstract ideas atthe very beginning of the book. In addition, we have included an Appendix which presents such basic ideas as set, function, and equivalence relation. We have found it most profitable not to dwell on these ideas independently, but to advise the students to read the Appendix when these ideas arise. Throughout the book we have included a great variety of

FAQs

What was the original purpose of writing Linear Algebra?

To provide a textbook for the undergraduate linear algebra course at MIT, primarily for mathematics majors at the junior level.

What is the main aim of revising the second edition?

To increase the range of courses that can be taught easily from the book, with structured chapter stop points and expanded material.

Which topics received the largest changes in the second edition?

Treatments of canonical forms and inner product spaces, including reorganizing material across Chapters 6–9.

Sep 14, 2026

Uploaded by Anda