  Quaternions, split quaternions, and hybrid numbers are very well-known number
systems. These number systems are used to make geometry in Euclidean and
Lorentz spaces. These number systems can be obtained with the help of a
quadratic form. This article examines how to find the corresponding number
system for any quadratic form. As a result of this examination, bilinear form,
vector product, skew-symmetric matrix, and rotation matrices corresponding to
any number system were obtained.
