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. > Presents matrix analysis in a novel framework > Tackles gradient analysis and optimization, a very topical subject matter > Provides new applications and perspectives of matrix analysis that are unique to this book Table 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.