Matrix Analysis and Applications (Hardcover)

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.

這本平衡且全面的研究以一個新的理論框架呈現矩陣分析的理論、方法和應用，讓讀者能夠以全新的角度理解二階和高階矩陣分析。除了矩陣分析的核心主題，如奇異值分析、矩陣方程的解和特徵分析，作者還介紹了本書獨有的新應用和觀點。梯度分析和優化這些非常熱門的主題在這裡扮演著核心角色。書中還包括子空間分析、投影分析和張量分析等在其他書籍中常常被忽略的主題。在為這個主題提供了堅實的基礎之後，作者特別強調矩陣分析在科學和工程中的眾多應用，使得這本書適合科學家、工程師和研究生閱讀。