Historical Research Of Vector Space Theory

With the development of vector theory, the vector space gradual development and maturing also become a necessity. On this basis, more abstract space developmented and formated. Through the study of historical documents at home and abroad, starting from the point of view of the general and summarized and detailed introduction to the historical development of the vector space. The main research results are as follows:â… . Detailed examination of the emergence and development of the theory of the vector. Start by the vector theory of the origin, the vector theory from the force and velocity vector of the parallelogram law theory, the Leibniz position geometric vector theory and from plural geometry represented in three areas. Focuses on the development of complete clues Vector theory in the modern sense:The complex geometric saidâ†'Hamiltonian quaternion to createâ†'Tate the quaternion developmentâ†'Maxwell criticism forâ†'Gibbs, founder of the theory of Heaviside vector.â…¡. Discussed the axiomatization of the vector space deeply. Set forth the history of the origin of the axiomatic method and practical significance, focus on Piano’s axiomatic method and the historical process of the vector space, Introduced the work of the Barbour, Schumacher, Weyl, Wiener etc. in vector space of axiomatic briefly.â…¢. Described the emergence and development of the vector space theory in detail. Since the linear equations is an important content in vector space, and the development of linear equations is inextricably linked with the history of the development of the theory of determinants, matrix theory development has greatly enriched the theory of linear space later, so we highlight the development of the theory of linear equations determinant and matrix theory, for linear correlation, independent base of vector group, the rank of the matrix such as the concept of fusion.â…£. Study the development of abstract space’s overview. With the development and the needs of real-world applications of mathematics, the mathematicians create more abstract space on the basis of the vector space’s development. This chapter focuses on the widely used Euclidean space, inner product spaces, normed vector space, Banach space, Hilbert space and briefly discusses the link between these spaces.