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This balanced and comprehensive study presents the theory, methods and applications of matrix analysis in a new theoretical framework, allowing readers to understand second-order and higher-order matrix analysis in a completely new light. Alongside the core subjects in matrix analysis, such as singular value analysis, the solution of matrix equations and eigenanalysis, the author introduces new applications and perspectives that are unique to this book. The very topical subjects of gradient analysis and optimization play a central role here. Also included are subspace analysis, projection analysis and tensor analysis, subjects which are often neglected in other books. Having provided a solid foundation to the subject, the author goes on to place particular emphasis on the many applications matrix analysis has in science and engineering, making this book suitable for scientists, engineers and graduate students alike.
List of contents
Preface; Notation; List of abbreviations; List of algorithms; Part I. Matrix Algebra: 1. Introduction to matrix algebra; 2. Special matrices; 3. Matrix differential; Part II. Matrix Analysis: 4. Gradient analysis and optimization; 5. Singular value analysis; 6. Solving matrix equations; 7. Eigenanalysis; 8. Subspace analysis and tracking; 9. Projection analysis; Part III. Higher-Order Matrix Analysis: 10. Tensor analysis; References; Index.
About the author
Xian-Da Zhang is Professor Emeritus in the Department of Automation at Tsinghua University, Beijing. He was a Distinguished Professor at Xidian University, Xi'an, China - a post awarded by the Ministry of Education of China, and funded by the Ministry of Education of China and the Cheung Kong Scholars Programme - from 1999 to 2002. His areas of research include signal processing, pattern recognition, machine learning and related applied mathematics. He has published over 120 international journal and conference papers, and seven books in Chinese. He taught the graduate course 'Matrix Analysis and Applications' at Tsinghua University from 2004 to 2011.
Summary
This balanced and comprehensive study presents the theory, methods and applications of matrix analysis in a new theoretical framework. The author also covers often neglected subjects, such as subspace analysis, projection analysis and tensor analysis, and even tackles the topical subject matter of gradient analysis and optimization.
Report
'Matrix analysis is the engine room of scientific computing since, inevitably, most computational problems are reduced to linear algebra. Xian-Da Zhang's monograph presents a thoroughly modern introduction to this important subject in a form suitable for its many users. Without taking liberties with mathematical content, the text privileges an algorithmic approach and ventures into new and important areas, e.g. tensor analysis. This is a valuable addition to any applied mathematician's bookshelf.' Arieh Iserles, University of Cambridge
