METHOD FOR CONSTRUCTING THE COMMUTATIVE ALGEBRA OF QUATERNION AND OCTONION
Ключевые слова:
hypercomplex number, quaternion, octonion, algebra, multiplication, division, commutativity, vector.Аннотация
In this paper, we solve the problem of constructing a commutative algebra of quaternions and
octonions. A proof of the theorem is given that the commutativity of quaternions can be ensured by specifying a set
of sign coefficients of the directions of reference of the angles between the radius vectors in the coordinate planes of
the vector part of the coordinate system of the quaternion space. The method proposed in the development of
quaternions possessing the commutative properties of multiplication is used further to construct a commutative
octonion algebra. The results obtained on improving the algebra of quaternions and octonions can be used in the
development of new hypercomplex numbers with division over the field of real numbers, and can also find
application for solving a number of scientific and technical problems in the areas of field theory, physical electronics,
robotics, and digital processing of multidimensional signals.
