Michael L. O'Leary - Linear Algebra

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Michael L. O’Leary

This edition first published 2021

© 2021 John Wiley and Sons, Inc.

All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, except as permitted by law. Advice on how to obtain permission to reuse material from this title is available at http://www.wiley.com/go/permissions.

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The contents of this work are intended to further general scientific research, understanding, and discussion only and are not intended and should not be relied upon as recommending or promoting scientific method, diagnosis, or treatment by physicians for any particular patient. In view of ongoing research, equipment modifications, changes in governmental regulations, and the constant flow of information relating to the use of medicines, equipment, and devices, the reader is urged to review and evaluate the information provided in the package insert or instructions for each medicine, equipment, or device for, among other things, any changes in the instructions or indication of usage and for added warnings and precautions. While the publisher and authors have used their best efforts in preparing this work, they make no representations or warranties with respect to the accuracy or completeness of the contents of this work and specifically disclaim all warranties, including without limitation any implied warranties of merchantability or fitness for a particular purpose. No warranty may be created or extended by sales representatives, written sales materials or promotional statements for this work. The fact that an organization, website, or product is referred to in this work as a citation and/or potential source of further information does not mean that the publisher and authors endorse the information or services the organization, website, or product may provide or recommendations it may make. This work is sold with the understanding that the publisher is not engaged in rendering professional services. The advice and strategies contained herein may not be suitable for your situation. You should consult with a specialist where appropriate. Further, readers should be aware that websites listed in this work may have changed or disappeared between when this work was written and when it is read. Neither the publisher nor authors shall be liable for any loss of profit or any other commercial damages, including but not limited to special, incidental, consequential, or other damages.

Library of Congress Cataloging‐in‐Publication Data

Names: O’Leary, Michael L., author.

Title: Linear algebra / Michael L. O’Leary.

Description: Hoboken, NJ : Wiley, 2021. | Includes bibliographical references and index.

Identifiers: LCCN 2021008522 (print) | LCCN 2021008523 (ebook) | ISBN 9781119437444 (hardback) | ISBN 9781119437475 (adobe pdf) | ISBN 9781119437604 (epub) | ISBN 9781119437437 (obook)

Subjects: LCSH: Algebras, Linear.

Classification: LCC QA184 .O425 2021 (print) | LCC QA184 (ebook) | DDC 512/.5-dc23

LC record available at https://lccn.loc.gov/2021008522

LC ebook record available at https://lccn.loc.gov/2021008523

Cover design by Wiley

Cover image: © Hank Erdmann/Shutterstock

For my niece, Lindsay

This book is an introduction to linear algebra. Its goal is to develop the standard first topics of the subject. Although there are many computations in the sections, which is expected, the focus is on proving the results and learning how to do this. For this reason, the book starts with a chapter dedicated to basic logic, set theory, and proof‐writing. Although linear algebra has many important applications ranging from electrical circuitry and quantum mechanics to cryptography and computer gaming, these topics will need to wait for another day. The goal here is to master the mathematics so that one is ready for a second course in the subject, either abstract or applied. This may go against current trends in mathematics education, but if any mathematical subject can stand onits own and be learned for its own sake, it is the amazing and beautiful linear algebra.

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