Applied Linear Algebra and Matrix Analysis

1. Front Matter

   Pages i-xii

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2. Linear Systems Of Equations

   Pages 1-54

3. Matrix Algebra

   Pages 55-144

4. Vector Spaces

   Pages 145-210

5. Geometrical Aspects Of Standard Spaces

   Pages 211-249

6. The Eigenvalue Problem

   Pages 251-304

7. Geometrical Aspects Of Abstract Spaces

   Pages 305-354

8. Back Matter

   Pages 355-383

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This book is about matrix and linear algebra, and their applications. For many students the tools of matrix and linear algebra will be as fundamental in their professional work as the tools of calculus; thus it is important to ensure that students appreciate the utility and beauty of these subjects as well as the mechanics. To this end, applied mathematics and mathematical modeling ought to have an important role in an introductory treatment of linear algebra. In this way students see that concepts of matrix and linear algebra make concrete problems workable. In this book we weave signi?cant motivating examples into the fabric of the text. I hope that instructors will not omit this material; that would be a missed opportunity for linear algebra! The text has a strong orientation toward numerical computation and applied mathematics, which means that matrix analysis plays a central role. All three of the basic components of l- ear algebra — theory, computation, and applications — receive their due. The proper balance of these components gives students the tools they need as well as the motivation to acquire these tools. Another feature of this text is an emphasis on linear algebra as an experimental science; this emphasis is found in certain examples, computer exercises, and projects. Contemporary mathematical software make ideal “labs” for mathematical experimentation. Nonetheless, this text is independent of speci?c hardware and software pl- forms. Applications and ideas should take center stage, not software.

• Eigenvalue
• Eigenvector
• Matrix
• algebra
• linear algebra
• matrix theory

From the reviews:

"The book under review is a nice blend of three independent components of linear algebra: Theory, computation and applications. … The book is consisting of the author preface, six chapters, table of symbols, solutions to selected exercises, a bibliography containing 13 references and subject index. … The book is very useful for undergraduate students and nonspecialists." (Mohammad Sal Moslehian, Zentralblatt MATH, Vol. 1128 (6), 2008)

"This book is intended for a one or two semester course, with emphasis on linear algebra as an experimental science. … The text is written in a nice conversational style. Proofs are provided for most results … . The author also provides many computer exercises, projects, and report topics … . Instructors wanting to encourage precision in mathematical writing will find these assignments helpful. … This is a good text for those who want to introduce their students to applied discrete mathematics … ." (Henry Ricardo, The Mathematical Association of America, September, 2008)

• University of Nebraska, 68588-0130, Lincoln, USA

  Thomas S. Shores

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