Cramer’s rules for various solutions to some restricted quaternionic linear systems

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• 作者：Guang-Jing Song ; Haixia Chang…
• 关键词：Quaternion matrix ; Cramer’s rule ; Generalized inverse $$A_{T{ ; }S}^{(2)}$$ A T ; S ( 2 ) ; Determinant ; System of linear equations ; 15A09 ; 15A24
• 刊名：Journal of Applied Mathematics and Computing
• 出版年：2015
• 出版时间：June 2015
• 年：2015
• 卷：48
• 期：1-2
• 页码：83-109
• 全文大小：534 KB
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• 作者单位：Guang-Jing Song (1)
  Haixia Chang (2)
  Zhongcheng Wu (3)
  
  1. School of Mathematics and Information Sciences, Weifang University, Weifang, 261061, People’s Republic China
  2. Department of Applied Mathematics, Shanghai Finance University, Shanghai, 201209, People’s Republic China
  3. School of fundamental studies, Shanghai University of Engineering Science, Shanghai, 201620, People’s Republic China
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Computational Mathematics and Numerical Analysis
  Applied Mathematics and Computational Methods of Engineering
  Theory of Computation
  Mathematics of Computing
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1865-2085

文摘

In this paper, we show some new necessary and sufficient conditions for the existences of the generalized inverses \(A_{r_{T_{1},S_{1}}}^{(2)}\) and \(A_{l_{T_{2},S_{2}}}^{(2)}\) over the quaternion skew field by checking the nonsingularity of some matrices instead of computing the direct sum of some quaternionic vector spaces. We also derive a series of concise determinantal representations of these generalized inverses. In addition, we give some condensed Cramer’s rules for the general solutions, the least squares solutions and the approximate solutions to some restricted quaternionic systems of linear equations, respectively.