Determinant Theory Of Historical Research

Determinants are useful tools in various branches of mathematics and have been indispensable in the modern physics as well as in other scientific fields. As a part of linear algebra, theory of determinants is of a long history. The purpose of this dissertation is to probe and to analyze systematically the historical development of theory of determinants on the basis of reading original sources and of investigating previous researches on the subject. The major contributions made in the dissertation are as follows.The evolution of theory of determinants is viewed for the first time in double lights-its development both in the West and in the East, and is systematized by being divided into three periods characterized as origin, founding, flourishing and improvement, and a distinct clue to describe the history of theory of determinants is thus presented.By all-sided use of comparative approach, the major contributions from the most representative authors in different periods of the Western history of theory of determinants are evaluated as objectively as possible. For example, full and accurate comparisons between Leibniz, Cramer and Maclaurin were made to show their respective influence. Maclaurin's contribution is emphasized here, which has been relatively overlooked in the past works on the history of theory of determinants. Again, by comparing Cauchy's work with his forerunners, special discussion were made for his function-theoretic approach and for his historic role as one of founders of the modern theory of determinants.Special attention is paid to the Japanese contributions towards theory of determinants. Not only the ideas and approaches of Seki Takakazu, but also the extension and improvement to Seki's work by his successors Iseki Tomotoki, Takebe Katahiro, Matunaga Yosisuke etc. are discussed in large details in comparison with each other and both the relativities and differences of their work are carefully analyzed. Furthermore, all those oriental achievements are compared with corresponding European results to display the different cultural backgrounds.Finally, the process of introduction of theory of determinants to China is briefly explored in the appendix.