Matrix Analysis and Applications

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.

• 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.

'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