Linear Algebra: Theory and Applications

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Motivated by their desire for a single text that meets the various requirements found in linear algebra courses, renowned writing team Ward Cheney and David Kincaid have developed this multi-faceted introduction to linear algebra. Focusing on a comprehensive blend of theory and application, this text guides theory-oriented mathematics students as they devise proofs and deal with abstraction. Likewise, this unique blend appeals to applications-oriented science and engineering students with its numerous problem sets that focus on understanding and learning vector spaces, matrices, linear transformations, and other tools of applied linear algebra. With its flexible design, Linear Algebra: Theory and Applications is an ideal resource for instructors who wish to choose what material to cover. The text includes over 3100 problems and homework assignments of great variety to support their choice. Key Features A flexible presentation allows instructors to use this text in a variety of course settings Numerous examples throughout the text show how problems from engineering, biology, natural science and demography can be solved using linear algebra. Students will learn course material thoroughly with over 3,100 true/false, multiple-choice, and computer-based projects and problems. The text encourages students to learn at least one of the powerful mathematical software tools such as Matlab®, Mathematics® and Maple® A Student Solutions Manual provides worked solutions to selected exercises from the text. About The Author Ward Cheney, PhD - University of Texas, Austin Ward Cheney’s research interests are in approximation theory and numerical analysis. His book Introduction to Approximation Theory has been in print for many years and has been translated into several languages. His book A Course in Approximation Theory, co-authored with Professor Will Light, is a graduate level textbook. Cheney has taught mathematics courses at the University of Kansas, Iowa State University, University of California at Los Angeles, Michigan State University, LundUniversity (Sweden), and The University of Texas at Austin. He has been the author or co-author of over 100 research papers. David R. Kincaid, PhD - University of Texas, Austin David Kincaid’s research interests are in scientific computing, especially parallel computing. He was one of the original co-authors for the BLAS: Basic Linear Algebra Subprograms. Previously co-authored books with Ward Cheney include Numerical Mathematics and Computing, currently in its 6th edition, and Numerical Analysis: Mathematics of Scientific Computing, in it’s 3rd edition. They have been translated into several languages as well as Braille and recorded for the visually impaired. Kincaid has taught computer science and mathematics courses at Purdue University and The University of Texas at Austin. He has been the author or co-author of over 100 research papers. Table of Contents Chapter 1: Systems Of Linear Equations Chapter 2: Vector Sub Spaces Chapter 3: Matrix Operations Chapter 4: Determinants Chapter 5: Vector Spaces Chapter 6: Eigensystems Chapter 7: Inner Product Vector Spaces Chapter 8: Additional Topics Appendix A: Deductive Reasoning And Proofs: Introduction Appendix B: Complex Arithmetic: Complex Numbers And Arithmetic References Index