Algebraic Properties of Reduced Biquaternions
Received:June 15, 2020  Revised:April 27, 2021
Key Word: reduced biquaternion   Moore-Penrose inverse   power function   root   exponential function  
Fund ProjectL:Supported by the National Natural Science Foundation of China (Grant No.11871379), Innovation Project of Department of Education of Guangdong Province (Grant No.2018KTSCX231) and Key project of National Natural Science Foundation of Guangdong Province Universities (Grant No.2019KZDXM025).
Author NameAffiliation
Wensheng CAO Department of Mathematics, Wuyi University, Guangdong 529020, P. R. China 
Zhe TANG Department of Mathematics, Wuyi University, Guangdong 529020, P. R. China 
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Abstract:
      In this paper, we study the algebraic properties of reduced biquaternions. With the aid of the real and complex matrix representations of reduced biquaternions, we introduce the concept of the Moore-Penrose inverse in reduced biquaternions. As applications, we solve the linear equations $ax=d$ and the quadratic equation $ax^2+bx+c=0$. By complex representation, we find the $n$th roots, the $n$th powers of a reduced biquaternion and obtain some properties of the matrix exponential of reduced biquaternion matrices.
Citation:
DOI:10.3770/j.issn:2095-2651.2021.05.001
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