| Algebraic Properties of Reduced Biquaternions |
| Received:June 15, 2020 Revised:April 27, 2021 |
| Key Words:
reduced biquaternion Moore-Penrose inverse power function root exponential function
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| Fund Project: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). |
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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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