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Mathematics
Article . 2024 . Peer-reviewed
License: CC BY
Data sources: Crossref
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Mathematics
Article . 2024
Data sources: DOAJ
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Solution to Several Split Quaternion Matrix Equations

descriptionPublicationkeyboard_double_arrow_right Article 30 May 2024 English Publisher:MDPI AGJournal:Mathematics, volume 12, page 1,707 (eissn: 2227-7390, Copyright policy )Funded by:NSERC | unidentified
Authors: Xin Liu; Tong Shi; Yang Zhang;

doi: 10.3390/math12111707

Solution to Several Split Quaternion Matrix Equations

Abstract

Split quaternions have various applications in mathematics, computer graphics, robotics, physics, and so on. In this paper, two useful, real representations of a split quaternion matrix are proposed. Based on this, we derive their fundamental properties. Then, via the real representation method, we obtain the necessary and sufficient conditions for the existence of solutions to two split quaternion matrix equations. In addition, two experimental examples are provided to show their feasibility.

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Keywords

matrix equation, split quaternions, real representation, QA1-939, <i>η</i>-conjugate, <i>η</i>-Hermitian, Mathematics

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
2
Top 10%
Average
Average
gold