Introductory Guide to Matrix Theory

Author: Zhuang Wajin
Publisher:
Publish Date: 2006-06-01
Features: The study of matrix over a field is one of the fundamental directions in the research of non-commutative algebra. This book discusses some of the major achievements made by Chinese scholars, represented by Professor Xie Bangjie, in this research direction since the 1970s and 1980s. The first chapter introduces the relevant basic knowledge; the second to fourth chapters elaborate on the fundamental theories of matrix equivalence, similarity, and isomorphism over a field, as well as the generalized inverse and eigenvalues of matrices over a field. The fifth chapter discusses the Dieudonné determinant and Xie Bangjie form determinant of matrices over a field, and provides a brief analysis of various determinant schemes for quaternion matrix algebras. The sixth and seventh chapters explore two research topics: quaternion matrices and matrix partial orders. Therefore, this book not only systematically presents the theory of general matrices over a field but also elaborates on the quaternion matrix theory with broad application prospects, as well as certain results on matrices over more general non-commutative principal ideal rings. This book can serve as a textbook for advanced undergraduate students in mathematics departments, as a reference for master's and doctoral students in algebra-related fields, or as a primary reference for their theses. It can also be used as a reference book for teachers and researchers in mathematics, mechanics, physics, and related disciplines.