Transform Linear Algebra

This book has evolved over many years, through taking and teaching courses on linear algebra to being involved in the linear algebra educational community, and by doing research in several related areas of mathematics. I started teaching linear algebra in 1965 during my second year at the University of Cologne, Germany, when I was asked to lead a recitation section for Prof. Dr. W. Jehne's freshman class. He, his staff, and Emil Artin's 1960/61 Hamburg lecture notes introduced me to Riesz's lemma, and as you will see, I have finally returned, with a view of my own. This book emphasizes the concepts of linear algebra and matrix theory. Teaching in this fashion is 'driven by the desire to convey the structure and nature of linear spaces and of linear transformations. Chapters 1 through 7 deal with linear transformations with respect to the standard unit vector basis. Starting with Chapter 7, we learn how to view and perceive each linear transformation more clearly with respect to its own specific basis. Almost every chapter has three sections. The first section contains a one(or two-) hour lecture, followed by problems. The second section deals with theoretical and mathematical enrichment, such as further concepts or alternative developments and proofs. The final section of each chapter details applications to and from linear algebra. My main aim is to help students develop an intuitive understanding of the subject and to present them with teachable and learnable concepts that lay out the foundations of linear algebra. This book is aimed at beginning or intermediate-level undergraduate students in engineering, science, and mathematics curricula. By stressing the importance of very few deliberate fundamental concepts throughout the lectures, I have tried to bring my students closer to understanding what linear algebra is all about and why there is such a need for learning and teaching it well. I am deeply indebted to my students for their patience and feedback, to my colleagues and my family, to Darrell for his expertise and help with tricky LATEX questions, to Rosie for her quick and expert typing of the first draft, to Achim for his critical reading, to Maria and Michael for checking the exercises and examples, and to the reviewers and editors. Frank Uhlig Auburn, Alabama, 2002Uhlig, Frank is the author of 'Transform Linear Algebra', published 2001 under ISBN 9780130415356 and ISBN 0130415359.