Abstract
Quaternions are a four-dimensional hypercomplex number system discovered by Hamilton in 1843 and next intensively applied in mathematics, modern physics, computer graphics and other fields. After the discovery of quaternions, modified quaternions were also defined in such a way that commutative property in multiplication is possible. That number system called as commutative quaternions is intensively studied and used for example in signal processing. In this paper we define generalized commutative quaternions and next based on them we define and explore Fibonacci type generalized commutative quaternions.
Highlights
One of the problems in applying quaternions is their noncommutative structure
Modified quaternions were proposed by Serge in [26], so that commutative property in multiplication is possible
Quaternions and commutative quaternions belong to the class of hypercomplex & Anetta Szynal-Liana aszynal@prz.edu.pl Iwona Włoch iwloch@prz.edu.pl
Summary
One of the problems in applying quaternions is their noncommutative structure. A different order of multiplication of quaternions results in different quaternions. That structure makes hard to conduct applications among other to engineering problems, see for example [22]. Modified quaternions were proposed by Serge in [26], so that commutative property in multiplication is possible. Quaternions and commutative quaternions belong to the class of hypercomplex
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