Miraculous hypercomplex numbers

Source abstract

<p>The development of the number system has been a long and difficult process, and many landmark concepts and theorems have been put forward. By briefly reviewing the development of hypercomplex systems, the rules for constructing 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 <strong>A</strong> constructed from the multiplication table satisfies the structure equation <strong>A</strong><sup>2</sup> = <em>n</em><strong>A</strong> and thus obtains a set of faithful matrix representations of the basic elements. This paper also uses typical examples to show the simple and clear concepts and wide application of hypercomplex numbers. Therefore, hypercomplex numbers are worth learning in basic education and applying in scientific research and engineering technology.</p>