Alan J. Laub
Matrix Analysis for Scientists and Engineers provides a blend of undergraduate and graduatelevel 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 oftenneeded bridge between undergraduatelevel matrix theory and linear algebra and the level of matrix analysis required for graduatelevel study and research. The text is sufficiently compact that the material can be taught comfortably in a onequarter or onesemester 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.
Audience
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 selfstudy 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.
Contents
Preface; Chapter 1: Introduction and Review; Chapter 2: Vector Spaces; Chapter 3: Linear Transformations; Chapter 4: Introduction to the Moore–Penrose 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.
See Sample Chapter: http://www.siam.org/books/textbooks/OT91sample.pdf
Read the review of this book that appeared in SIAM Review.
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2005 / xiv + 157 pages / Softcover / ISBN13: 9780898715767 / ISBN10: 0898715768 / List Price $46.00 / SIAM Member Price $32.20 / Order Code OT91
