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Matrix Analysis for Scientists and Engineers

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by Alan J. Laub


2005 / xiv + 157 pages / Softcover / ISBN: 978-0-898715-76-7 / List Price $50.00 / SIAM Member Price $35.00 / Order Code OT91

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Matrix Analysis for Scientists and Engineers provides a blend of undergraduate- and graduate-level topics in matrix theory and linear algebra that relieves instructors of the burden of reviewing such material in subsequent courses that depend heavily on the language of matrices. Consequently, the text provides an often-needed bridge between undergraduate-level matrix theory and linear algebra and the level of matrix analysis required for graduate-level study and research. The text is sufficiently compact that the material can be taught comfortably in a one-quarter or one-semester course.

Throughout the book, the author emphasizes the concept of matrix factorization to provide a foundation for a later course in numerical linear algebra. The author addresses connections to differential and difference equations as well as to linear system theory and encourages instructors to augment these examples with other applications of their own choosing.

Because the tools of matrix analysis are applied on a daily basis to problems in biology, chemistry, econometrics, engineering, physics, statistics, and a wide variety of other fields, the text can serve a rather diverse audience. The book is primarily intended to be used as a text for senior undergraduate or beginning graduate students in engineering, the sciences, mathematics, computer science, or computational science who wish to be familiar enough with matrix analysis and linear algebra that they can effectively use the tools and ideas of these fundamental subjects in a variety of applications. However, individual engineers and scientists who need a concise reference or a text for self-study will also find this book useful.

Prerequisites for using this text are knowledge of calculus and some previous exposure to matrices and linear algebra, including, for example, a basic knowledge of determinants, singularity of matrices, eigenvalues and eigenvectors, and positive definite matrices. There are exercises at the end of each chapter.

Preface; Chapter 1: Introduction and Review; Chapter 2: Vector Spaces; Chapter 3: Linear Transformations; Chapter 4: Introduction to the MooreÐPenrose Pseudoinverse; Chapter 5: Introduction to the Singular Value Decomposition; Chapter 6: Linear Equations; Chapter 7: Projections, Inner Product Spaces, and Norms; Chapter 8: Linear Least Squares Problems; Chapter 9: Eigenvalues and Eigenvectors; Chapter 10: Canonical Forms; Chapter 11: Linear Differential and Difference Equations; Chapter 12: Generalized Eigenvalue Problems; Chapter 13. Kronecker Products; Bibliography; Index.

ISBN: 9780898715767

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