The additional material in this edition should permit instructors to prepare an under graduate course in Numerical Linear Algebra for students who have not previously studied numerical Analysis. This could be done by covering Chapters 1, 6, 7, and 9, and then, as time permits, including other material of the instructor's choice Acknowledgments We have been fortunate to have had many of our students and colleagues give us their that essions of earlier editions of this book. We have tried to include all the suggestions that complement the philosophy of the book, and we are extremely grateful to all those who have taken the time to contact us about ways to improve subsequent versions We would particularly like to thank the following, whose suggestions we have used in this and previous editions John Carroll, Dublin City University (Ireland) Gustav Delius, University of York (UK) Pedro Jose Paul Escolano, University of Sevilla(Spain) Warren Hickman, Westminster College Jozsi Jalics, Youngstown State University Dan Kalman, American University Robert Lantos, University of Ottawa( Canada) Eric Rawdon, Duquesne University illip Schmidt, University of Northern Kentucky Kathleen Shannon, Salisbury Ur Roy Simpson, State University of New York, Stony Brook Dennis C Smolarski, Santa Clara University James Verner, Simon Fraser University( Canada) Andre Weideman, University of Stellenbosch(South Africa) Joan Weiss, Fairfield University of massachusetts at Amherst Dick Wood, Seattle Pacific University George Yates, Youngstown State University As has been our practice in past editions of the book, we used undergraduate student elp at Youngstown State University in preparing the ninth edition. Our assistant for this edition was Mario Sracic, who checked the new Maple code in the book and worked as our in-house copy editor. In addition, Edward Burden has been checking all the programs that accompany the text. We would like to express gratitude to our colleagues on the faculty and Copyright 2010 Cengage Learning. All Rights t materially affect the overall leaming eaperience Cengage Learning reserves the right to remo rty commen may be suppressed from the eBook andor eChaptert'sh. May no be copied, scanned, or duplicated, in whole or in part Due toPreface xiii The additional material in this edition should permit instructors to prepare an under￾graduate course in Numerical Linear Algebra for students who have not previously studied Numerical Analysis. This could be done by covering Chapters 1, 6, 7, and 9, and then, as time permits, including other material of the instructor’s choice. Acknowledgments We have been fortunate to have had many of our students and colleagues give us their impressions of earlier editions of this book. We have tried to include all the suggestions that complement the philosophy of the book, and we are extremely grateful to all those who have taken the time to contact us about ways to improve subsequent versions. We would particularly like to thank the following, whose suggestions we have used in this and previous editions. John Carroll, Dublin City University (Ireland) Gustav Delius, University of York (UK) Pedro José Paúl Escolano, University of Sevilla (Spain) Warren Hickman, Westminster College Jozsi Jalics, Youngstown State University Dan Kalman, American University Robert Lantos, University of Ottawa (Canada) Eric Rawdon, Duquesne University Phillip Schmidt, University of Northern Kentucky Kathleen Shannon, Salisbury University Roy Simpson, State University of New York, Stony Brook Dennis C. Smolarski, Santa Clara University Richard Varga, Kent State University James Verner, Simon Fraser University (Canada) André Weideman, University of Stellenbosch (South Africa) Joan Weiss, Fairfield University Nathaniel Whitaker, University of Massachusetts at Amherst Dick Wood, Seattle Pacific University George Yates, Youngstown State University As has been our practice in past editions of the book, we used undergraduate student help at Youngstown State University in preparing the ninth edition. Our assistant for this edition was Mario Sracic, who checked the new Maple code in the book and worked as our in-house copy editor. In addition, Edward Burden has been checking all the programs that accompany the text. We would like to express gratitude to our colleagues on the faculty and Copyright 2010 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it