A Research Of The Matrix Theory

As a fundamental concept and an important object of study, the matrix theory has many applications in various mathematics branches as well as in other scientific fields. The purpose of this dissertation is to analyze the development of the matrix theory according to two clues in chronological sequence and ideological progress based on analysis of original materials and investigation of previous researches in this field. The main results gained in this dissertation are as follows:1. The process and ideology in seeds of the matrix theory are elaborated in detail. The seeds of the matrix theory has a long history, and the Suanchou in"Nine Chapters of Arithmetic" was the earliest embryonic form of matrix. The rudiment of matrix in the ancient China has condensed abundant mathematics thoughts and methods, propelled political and economic development of Chinese society, and held important status in the world mathematics history. As a permutation form, the matrix concept has only solved practical problems because it hasn't been the matrix theory independence.2. The course of development in earlier period and the matrix theory of important mathematicians are discussed in great detail. Historical background of the society and culture is described, the matrix thought accompanying the work of quadratic form differential equation and determinant is pointed out, and J.J.Sylvester's matrix theory in the earlier period is elaborated. The matrix theory originated from the 18^th century and built in the 19^th century in booky form. J.J.Sylvester first used the word "Matrix", introduced some fundamental concepts related to matrix, obtained some principal results and famous theorems, and made important contributions for the matrix theory.3. The process of the foundation and the formation of the matrix theory is inspected in great detail. The matrix theory which A.cayley J.J.Sylvester and G.Frobenius founded is elaborated, and its influence is introduced. Many mathematicians did such a great mass of work that the matrix theory completed a ripe system from scraps of information. As the originator of the matrix theory, A. Cayley first separated matrix from determinant or system of equations and started to study. A. Cayley, J.J.Sylvester and others developed the matrix theory, laid a foundation of the invariant theory, and G. Frobenius did an indispensable contribution. 4. The latter development and applications of the matrix theory are inspected. A.Cayley's modern thought that looked matrix upon as a hypercomplex developed to the early days of the 20^th century from the end of the 19^th century. Infinite matrix theory and the matrix theory on abstract region investigated further since the development on integral equation and modern physics. Up till now, the matrix theory has many mathematics branches such as matrix equations, matrix factorization, generalized inverse matrix and so on.5. The spread of matrix theory in China is elaborated. The condition of algebra development of the 19^th century in China is described generality, and the course of spread of matrix theory in China is inspected. The seeds of matrix lay in China, but the scholars in Chinese history didn't study as an independent object and raise experience to the level of theory yet. After the 1850's, the matrix theory was selected in China follow the Western cream of mathematics under the circumstances of translation, education, study and others.