دانلود کتاب نظریه ماتریس، نتایج و تکنیک‌های پایه، ویرایش سوم

Over the years, as I revised and expanded this book, my goal has remained the same: to provide a comprehensive text for a second course in linear algebra and matrix theory where many topics are covered briefly. This text is intended for advanced undergraduate and early graduate students. Through this course, students learn, practice, and master fundamental matrix results and techniques—what I like to call matrix kung fu—which are essential for applications in various fields, including mathematics, statistics, physics, computer science, data science, engineering, etc. I also hope that the book serves as a valuable reference for researchers in the field as well as for those who use matrices.
This edition introduces more than 200 examples. These examples help make theoretical concepts—such as theorems and proofs—more accessible to students. Additionally, this edition includes approximately 1,500 exercises of varying difficulty levels. With a focus on basic matrix theory and an emphasis on partitioned matrices, this edition significantly revises and expands upon its predecessors.
Matrix theory (or a second course in linear algebra) can be approached in various ways. The material in this text reflects my own interests and preferences: The results are basic, important, and elegant. While the content is condensed, I strive to make it clear, concise, and accessible.
Covering all chapters in detail in a semester class is impractical. The first five chapters establish fundamental concepts, while Chapters 6–9 focus on special matrices, including unitary, positive semidefinite, Hermitian, and normal matrices. Chapter 10 explores majorization inequalities (of eigenvalues, singular values, di-agonal entries, and norms), which can be used as a supplementary material or as a graduate-level topic in pure or applied mathematics.