In mathematics, the hypercomplex number is a traditional term for an element of a finite-dimensional unital algebra over the field of real numbers. The study of hypercomplex numbers in the late 19th …

According to van der Waerden (1985), a hypercomplex number is a number having properties departing from those of the real and complex numbers. The most common examples are biquaternions, …

The meaning of HYPERCOMPLEX is of, relating to, or being a general form of number that can be expressed as a vector of n dimensions in the form x1e1 + x2e2 + … + xnen where the coefficients …

In summary, this study presents a comprehensive generalization of complex numbers and the Euler identity in higher dimensions, shedding light on the geometric properties of vectors within these …

Jul 7, 1997 · The hypercomplex numbers are a generalization of the complex numbers. They were created in an attempt to describe certain geometric operations in spaces with a dimension higher …

In this section, we present the basics of the complex and hypercomplex numbers, namely quaternions, and describe the main operations and properties of such numbers.

The concept of a hypercomplex number covered them all, and called for a discipline to explain and classify them. The cataloguing project began in 1872 when Benjamin Peirce first published his Linear …

Hypercomplex numbers, such as quaternions and octonions, expand be-yond traditional real and complex numbers by introducing additional imaginary units.

Mar 1, 2026 · The best-known hypercomplex number systems are the 4-dimensional quaternions, 8-dimensional octonions, and 16-dimensional sedenions, as summarized in the table below along with …

View Courses or the Academic Calendar. The course should appeal to those seeking a better understanding of the arithmetical underpinnings of our number system. A survey of those systems of …