Miraculous Hypercomplex Numbers

Abstract

<p>The development of number system has gone through a long and difficult process, and many landmark concepts and theorems were put forward. By briefly reviewing the development of hypercomplex systems, the constructing rules of the unit elements are discussed. As a vector space defining multiplication, division and norm of vectors, hypercomplex numbers synthesize the advantages of mathematical tools such as algebra, geometry and analysis, faithfully describe the intrinsic properties of space-time and physical systems, and provide a unified language and a powerful tool for basic theories and engineering technology. In the application of hypercomplex numbers, the group-like properties of the basis vectors are the most important, and the zero factor has little influence on the algebraic operation. The multiplication table of the basis vectors fully describes the intrinsic properties of the hypercomplex system, and the matrix A constructed from the multiplication table satisfies the structure equation A<sup>2</sup> = nA, and thus obtains a set of faithful matrix representations of the basis elements. Th/is paper also uses typical examples to show the simple and clear concepts and wide application of hypercomplex numbers. Therefore, hypercomplex numbers are worth of learning in basic education and appling in scientific research and engineering technology</p>